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Algebraic structure
Noetherian rings can be extended to finitely presented modules over coherent rings. Every left Noetherian ring is left coherent. The ring of polynomials
Coherent_ring
Generalization of vector bundles
coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector
Coherent_sheaf
In algebra, module with a finite generating set
and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules
Finitely_generated_module
a ring spectrum is often called perfect; see also module spectrum. When the structure sheaf O X {\displaystyle {\mathcal {O}}_{X}} is not coherent, working
Perfect_complex
Algebraic structure in ring theory
general be flat. In fact, given a ring R, every direct product of flat R-modules is flat if and only if R is a coherent ring (that is, every finitely generated
Flat_module
Mathematical concept
Noetherian integral domain is a Dedekind ring with a torsion class group. A coherent ring is a commutative ring with each finitely generated ideal finitely
Overring
wavelength 3.6 cm near ring's apoapsis. Such strong scattering requires the existence of a coherent structure. That the ε ring does have such a fine structure
Rings_of_Uranus
problems considered here make sense only for a Noetherian ring, or at least a coherent ring. In fact, this article is restricted to Noetherian integral
Linear_equation_over_a_ring
Space homeomorphic to some ring spectrum
the spectrum of a commutative ring. It is sometimes also called a coherent space because of the connection to coherent topoi. Let X be a topological space
Spectral_space
A coherent ring is a ring that is a coherent module over itself. complete 1. A local complete intersection ring is a Noetherian local ring whose completion
Glossary of commutative algebra
Glossary_of_commutative_algebra
left coherent ring is a ring such that every finitely generated left ideal of it is a finitely presented module; in other words, it is coherent as a left
Glossary_of_ring_theory
Modern form of the metric system
intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always
International_System_of_Units
Brazilian computer engineer
Arrays (FPGA 95), Monterey, CA, February 1995. The Performance of Cache-Coherent Ring-based Multiprocessors. Luiz André Barroso and Michel Dubois. In Proceedings
Luiz_André_Barroso
Sheaf of rings in mathematics
mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that
Ringed_space
Generalisations of Serre duality in mathematics
In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex
Coherent_duality
Literary analysis
The task of constructing The Lord of the Rings was long and complex, lasting from its start in 1937, soon after the success of J. R. R. Tolkien's children's
Constructing The Lord of the Rings
Constructing_The_Lord_of_the_Rings
High-speed interconnect standard for shared memory multiprocessing and message passing
The Scalable Coherent Interface or Scalable Coherent Interconnect (SCI), is a high-speed interconnect standard for shared memory multiprocessing and message
Scalable_Coherent_Interface
Instrument to measure angular velocity
A ring laser gyroscope (RLG) consists of a ring laser having two independent counter-propagating resonant modes over the same path; the difference in
Ring_laser_gyroscope
provable; There are many examples of coherent/geometric theories: all algebraic theories, such as group theory and ring theory, all essentially algebraic
Geometric_logic
Optical effect
have been proposed for this observational phenomenon: shadow hiding and coherent backscatter. The phase angle is defined as the angle between the observer
Opposition_surge
Concept in algebraic geometry
analogous notion of a coherent algebraic sheaf on a scheme. In both cases, the given space X {\displaystyle X} comes with a sheaf of rings O X {\displaystyle
Coherent_sheaf_cohomology
Concept in algebraic geometry
about Noetherian rings and Noetherian schemes is the dévissage theorem. This makes it possible to decompose arguments about coherent sheaves into inductive
Noetherian_scheme
Generalization of algebraic variety
particular, a module M over a commutative ring R determines an associated OX-module ~M on X = Spec(R). A quasi-coherent sheaf on a scheme X means an OX-module
Scheme_(mathematics)
1998 Japanese film
the Ring series. S is canonically a sequel to the novel Spiral that this film is an adaptation of. That being said, the film has little coherent continuity
Spiral_(1998_film)
Sheaf consisting of modules on a ringed space; generalizing vector bundles
quasi-coherent sheaves, and in fact, on affine or projective schemes, all quasi-coherent sheaves are obtained this way. Sheaves of modules over a ringed space
Sheaf_of_modules
Literary device in Tolkien's fiction
Scholars have described the narrative structure of The Lord of the Rings, a high fantasy work by J. R. R. Tolkien published in 1954–55, in a variety of
Narrative structure of The Lord of the Rings
Narrative_structure_of_The_Lord_of_the_Rings
Device used in sexual situations
although it will make it somewhat more difficult for the wearer to produce coherent speech. Occasionally, reins are attached. Because of the possibility of
Gag_(BDSM)
Technique from algebraic geometry
stacks, flat descent is exactly the statement that the prestack of quasi-coherent sheaves is a stack with respect to étale (or fpqc) topology. "Vanilla"
Faithfully_flat_descent
in a ring. The ideal sheaves on a geometric object are closely connected to its subspaces. Let X be a topological space and A a sheaf of rings on X.
Ideal_sheaf
Mathematical ring with well-behaved ideals
are also true. A left Noetherian ring is left coherent and a left Noetherian domain is a left Ore domain. (Bass) A ring is (left/right) Noetherian if and
Noetherian_ring
Spectroscopy used in chemistry and physics
Coherent anti-Stokes Raman spectroscopy, also called Coherent anti-Stokes Raman scattering spectroscopy (CARS), is a form of spectroscopy used primarily
Coherent anti-Stokes Raman spectroscopy
Coherent_anti-Stokes_Raman_spectroscopy
Theorem in algebra mathematics
relating projective modules and coherent sheaves. More generally, one has Let R {\displaystyle R} be a local ring and M {\displaystyle M} a finitely
Nakayama's_lemma
Set of a ring's prime ideals
commutative ring is naturally endowed with a sheaf of commutative rings, called the structure sheaf, which makes it a ringed space; that is, commutative rings are
Spectrum_of_a_ring
Multi-scale chaotic motions
Some coherent structures, such as vortex rings, etc. can be large-scale motions comparable to the extent of the shear flow. There are also coherent motions
Coherent_turbulent_structure
Radio dramatisation of book
The Lord of the Rings 1981 radio series is an epic fantasy adventure for BBC Radio 4, adapted from J. R. R. Tolkien's 1955 novel of the same name. It
The Lord of the Rings (1981 radio series)
The_Lord_of_the_Rings_(1981_radio_series)
Projective analogue of the spectrum of a ring
algebra as a ring. Here we assume that S 0 = O X {\displaystyle S_{0}=O_{X}} . We make the additional assumption that S is a quasi-coherent sheaf; this
Proj_construction
Tool to track locally defined data attached to the open sets of a topological space
algebraic geometry, namely quasi-coherent sheaves. Here the topological space in question is the spectrum of a commutative ring R {\displaystyle R} , whose
Sheaf_(mathematics)
2026 film by Boots Riley
shopworn than his more innovative swerves [...] at the expense of a more coherent and biting political message." The Guardian's Radheyan Simonpillai gave
I_Love_Boosters
Branch of mathematics
commutative rings is being replaced with a ∞-category of "derived rings." In classical algebraic geometry, the derived category of quasi-coherent sheaves
Derived_algebraic_geometry
through ν. An analytic space is coherent if its structure sheaf O {\displaystyle {\mathcal {O}}} is a coherent sheaf. A coherent sheaf of O {\displaystyle {\mathcal
Analytic_space
Algebra of complex square matrices
scheme. A coherent algebra forms a principal ideal ring under Schur product; moreover, a commutative coherent algebra forms a principal ideal ring under ordinary
Coherent_algebra
Cohomology class
In mathematics, a highly structured ring spectrum or A ∞ {\displaystyle A_{\infty }} -ring is an object in homotopy theory encoding a refinement of a multiplicative
Highly structured ring spectrum
Highly_structured_ring_spectrum
Diffraction pattern in optics
the series of concentric rings around is called the Airy pattern. Both are named after George Biddell Airy. The disk and rings phenomenon had been known
Airy_disk
Branch of mathematics
theorem of Jean-Pierre Serre, quasi-coherent sheaves on Proj of a graded ring are the same as graded modules over the ring up to finite dimensional factors
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Tool in mathematical dimension theory
algebras, and graded or filtered modules over these algebras, as well as to coherent sheaves over projective schemes. The typical situations where these notions
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
Collection of J. R. R. Tolkien's mythopoeic works
selecting and arranging in such a way as seemed to me to produce the most coherent and internally self-consistent narrative." Among the difficulties was that
The_Silmarillion
Romanian-American mathematician and mathematical poet
2017. Glaz is the author of a book on commutative algebra, Commutative Coherent Rings (Lecture Notes in Mathematics 1371, Springer, 1989). She is an editor
Sarah_Glaz
In algebraic geometry, a Noetherian local ring R is called parafactorial if it has depth at least 2 and the Picard group Pic(Spec(R) − m) of its spectrum
Parafactorial_local_ring
Topics referred to by the same term
Grothendieck duality may refer to: Coherent duality of coherent sheaves Grothendieck local duality of modules over a local ring This disambiguation page lists
Grothendieck_duality
Topics referred to by the same term
angle. Tensor Ring, a closed-loop device (often copper) utilizing cubit-length geometry to generate a stabilized energy column or coherent tensor field
Toroidal
cohomology of modules over local rings, analogous to Serre duality of coherent sheaves. Suppose that R is a Cohen–Macaulay local ring of dimension d with maximal
Grothendieck_local_duality
National laboratory in New York, United States
Nanoprobe (HXN) 5-ID: Submicron Resolution X-ray Spectroscopy (SRX) 9-ID: Coherent Diffractive Imaging (CDI) 18-ID: Full-Field X-ray Imaging (FXI) 26-ID-1:
National Synchrotron Light Source II
National_Synchrotron_Light_Source_II
Complex, ringlike filament of stars wrapped around the Milky Way
the Monoceros Ring, but the authors indicate that it might also be compatible with the existence of an unrelated kinematically coherent structure. List
Monoceros_Ring
Synchrotron light sources
storage rings (DLSR), or ultra-low emittance storage rings, are synchrotron light sources where the emittance of the electron-beam in the storage ring is smaller
Diffraction-limited storage ring
Diffraction-limited_storage_ring
Mountain in United States of America
Ring Mountain is an elevated landform on the Tiburon Peninsula in Marin County, California. This mountain was named for George E. Ring, who served as a
Ring_Mountain_(California)
Type of particle accelerator
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating, typically for many hours
Storage_ring
is the quasi-coherent sheaf of ideals cutting out Z, then the direct image i ∗ {\displaystyle i_{*}} from the category of quasi-coherent sheaves over
Closed_immersion
Type of commutative ring in mathematics
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality
Cohen–Macaulay_ring
all local rings are Cohen-Macaulay. For example, regular schemes, and Spec k[x,y]/(xy) are Cohen–Macaulay, but is not. coherent sheaf A coherent sheaf on
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Open standard processor interconnection for data centers
includes PCIe-based block input/output protocol (CXL.io) and new cache-coherent protocols for accessing system memory (CXL.cache) and device memory (CXL
Compute_Express_Link
Type of ringed space
a ringed space X is a sheaf of commutative rings on X that is also a sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules. It is quasi-coherent if
Sheaf_of_algebras
Literary analysis
J. R. R. Tolkien's The Lord of the Rings has been translated, with varying degrees of success, into dozens of languages from the original English. He
Translating The Lord of the Rings
Translating_The_Lord_of_the_Rings
Concept in quantum mechanics
one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose
Particle_in_a_ring
Simplicial set constructed from the objects and morphisms of a small category
of an ∞-category Like a nerve functor, but more generally, the homotopy coherent nerve functor associates to a simplicially enriched category a simpllicial
Nerve_(category_theory)
English writer and philologist (1892–1973)
author of the high fantasy works The Hobbit (1937) and The Lord of the Rings (1954–1955). From 1925 to 1945 Tolkien was the Rawlinson and Bosworth Professor
J._R._R._Tolkien
Literary work by J. R. R. Tolkien
backstory to The Lord of the Rings". In Kane's view, this fails to recognise the value of the material; fails to establish "a coherent narrative"; and fails
The_Fall_of_Númenor
Research apparatus for particle physics
Laboratory. Electrons propagating through a magnetic field emit very bright and coherent photon beams via synchrotron radiation. It has numerous uses in the study
Particle_accelerator
In algebraic geometry, a local ring A is said to be unibranch if the reduced ring Ared (obtained by quotienting A by its nilradical) is an integral domain
Unibranch_local_ring
Branch of mathematics
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology
K-theory
Mexican boxer (born 1962)
multiple-time world champion in three weight divisions, Chávez was listed by The Ring magazine as the world's best boxer, pound for pound, from 1990 to 1993. During
Julio_César_Chávez
British physicist (1918–1994)
many inventions led to daily use worldwide. These include zoom lenses, coherent fibre-optics, and rod-lens endoscopes, which were used in keyhole surgery
Harold_Hopkins_(physicist)
commutative ring is a Dedekind domain if and only if it is a Prüfer domain and Noetherian. Though Prüfer domains need not be Noetherian, they must be coherent, since
Prüfer_domain
Method of strengthening materials by changing grain size
alloys. Coherent IPBs, in particular, can provide additional barriers to dislocation motion, similar to grain boundaries. In contrast, non-coherent IPBs
Grain_boundary_strengthening
Type of Abelian category (in category theory in mathematics)
presented. (This generalizes the notion of coherent sheaves on a ringed space.) The full subcategory of all coherent objects in A {\displaystyle {\cal {A}}}
Grothendieck_category
Research center at Stanford University
A portion of the original linear accelerator is now part of the Linac Coherent Light Source. The Stanford Linear Collider was a linear accelerator that
SLAC National Accelerator Laboratory
SLAC_National_Accelerator_Laboratory
Generic flatness Irrelevant ideal Locally ringed space Coherent sheaf Invertible sheaf Sheaf cohomology Coherent sheaf cohomology Hirzebruch–Riemann–Roch
List of algebraic geometry topics
List_of_algebraic_geometry_topics
commutative rings are replaced with derived versions such as differential graded algebras, commutative simplicial rings, or commutative ring spectra. From
Derived_scheme
Cryptography secured against quantum computers
such as learning with errors, ring learning with errors (ring-LWE), the ring learning with errors key exchange and the ring learning with errors signature
Post-quantum_cryptography
Physics apparatus designed to study neutrinos
individual nucleons, in a process known as coherent neutral current neutrino-nucleus elastic scattering or coherent neutrino scattering. This effect has been
Neutrino_detector
Short, constantly recurring musical phrase
even a simple rhythm. Leitmotifs can help to bind a work together into a coherent whole, and also enable the composer to relate a story without the use of
Leitmotif
Plasma and magnetic field structure
A plasmoid is a coherent structure of plasma and magnetic fields. Plasmoids have been proposed to explain natural phenomena such as ball lightning, magnetic
Plasmoid
Algebraic variety in a projective space
scheme over a field (or, more generally over a Noetherian ring A). Cohomology of coherent sheaves F {\displaystyle {\mathcal {F}}} on X satisfies the
Projective_variety
Equivalence relation on rings
equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings R, S are Morita equivalent (denoted
Morita_equivalence
"Smallest" commutative algebra that contains a vector space
S(V) can be identified, through a canonical isomorphism, to the polynomial ring K[B], where the elements of B are considered as indeterminates. Therefore
Symmetric_algebra
Technique for patterning photomasks
Interference lithography (or holographic lithography) is a technique that uses coherent light (such as light from a laser) for patterning regular arrays of fine
Interference_lithography
Noetherian graded ring generated by degree-one elements, then the Proj of R in this sense is equivalent to the category of coherent sheaves on the usual
Noncommutative projective geometry
Noncommutative_projective_geometry
In mathematics, a mapping between categories
R} determined by a ring homomorphism ϕ : R → S {\displaystyle \phi :R\to S} , then the direct image functor f∗ on quasi-coherent sheaves identifies with
Direct_image_functor
The latter version is described as an indirect quote of Adenauer's last coherent statement. Incorrectly reported as, "Put me back on my bloody bike." Also
List of last words (20th century)
List_of_last_words_(20th_century)
Scottish physicist and mathematician (1831–1879)
Natural Philosophy at Marischal College in Aberdeen, where he studied the rings of Saturn and correctly proposed that they were composed of numerous small
James_Clerk_Maxwell
In algebra, a module over a ring
In algebra, a free presentation of a module M over a commutative ring R is an exact sequence of R-modules: ⨁ i ∈ I R → f ⨁ j ∈ J R → g M → 0. {\displaystyle
Free_presentation
Diode that emits light from an organic compound
manufacturing costs, poor stability, short life, and other shortcomings. Coherent emission from a laser dye-doped tandem SM-OLED device, excited in the pulsed
OLED
2003 film by David Zucker
Washington, the film parodies a number of early 2000s films, including The Ring (2002), Signs (2002), The Matrix Reloaded (2003), and 8 Mile (2002). The
Scary_Movie_3
principle wavefunction collapse zero-point energy bound state coherent state squeezed coherent state density state Fock state, Fock space vacuum state quasinormal
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
1981 film by John Boorman
Excalibur's visual style, though some felt it came at the expense of a coherent plot or character depth. It won the award for Best Artistic Contribution
Excalibur_(film)
Term in algebraic geometry
showed that the higher direct images preserve coherent analytic sheaves.) As a very special case: the ring of regular functions on a proper scheme X over
Proper_morphism
Invariant of algebraic varieties and of more general schemes
schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. Some of the deepest problems in algebraic
Motivic_cohomology
American sports and entertainment promoter
world’s new premier Brazilian Jiu-Jitsu live event series". On June 23, 2025, Ring Magazine officially announced that TKO's boxing promotion (earlier announced
TKO_Group_Holdings
American multinational technology conglomerate
Amazon Lab126, a computer hardware R&D provider. Other subsidiaries include Ring, Twitch, IMDb, and Whole Foods Market. Its acquisition of Whole Foods in
Amazon_(company)
Anthology of literary criticism of Tolkien
the Rings is a collection of scholarly essays on J. R. R. Tolkien's Middle-earth writings, mainly concerning his fantasy novel The Lord of the Rings. It
Understanding The Lord of the Rings
Understanding_The_Lord_of_the_Rings
Electricity generation by nuclear fusion
However beam systems cannot be used for power because keeping a beam coherent takes more energy than comes from fusion. Many approaches, equipment, and
Fusion_power
COHERENT RING
COHERENT RING
Boy/Male
Tamil
God gift, Inherent, Inscribed into something, Within something
Boy/Male
French
Adherent of a nobleman.
Boy/Male
French American Teutonic English German
Adherent of a nobleman.
Boy/Male
Hindu
God gift, Inherent, Inscribed into something, Within something
Boy/Male
Arabic, Muslim, Sindhi
Donation; Grant; Gift; Inherent; Giving; Similar to Wahb
Girl/Female
Hebrew
Sparkle.
Surname or Lastname
English
English : from the Old English personal name Hringwulf.German : from a short form of a Germanic personal name based on hring ‘ring’.German : metonymic occupational name for a ring maker (see Ringler).German : altered spelling of Ringel, an Old Prussian personal name.
Boy/Male
American, Australian, British, Celtic, Christian, English, Greek
Noble; Rock; Adherent of the Goddess Artemis; Bear Man; Eagle of Thor
Boy/Male
French Teutonic
Adherent of a nobleman.
Boy/Male
Australian, Greek
Adherent of the Goddess Artemis
Surname or Lastname
English
English : ethnic name from Old French Lohereng ‘man from Lorraine’ (see Lorraine).
Boy/Male
Tamil
God gift, Inherent, Inscribed into something, Within something
Surname or Lastname
English
English : of uncertain origin. It is first attested in Norwich in 1259 as Ringerose, and later forms show no significant variantion. Unless it had already been drastically altered by folk etymology at that early date, it is probably from Middle English ring ‘ring’ + rose ‘rose’, but if so the original meaning is far from clear.
Boy/Male
Arabic, Muslim, Sindhi
Gift; Inherent; Giving Donation; Grant
Surname or Lastname
English and German
English and German : variant of Ring 1.Perhaps a Rhenish short form of the Latin personal name Quirinus.
Boy/Male
American, Australian, British, Celtic, Chinese, Christian, English, German, Greek, Irish
Rock; Bear; Adherent of the Goddess Artemis; Bear Man; Eagle of Thor
Boy/Male
Indian, Telugu
Inherent; Inscribed into Something; Within Something
Boy/Male
Hindu
God gift, Inherent, Inscribed into something, Within something
Boy/Male
French English German
Adherent of a nobleman.
Boy/Male
American, Australian, British, English, French, German
God's Protection; Variant of Anseim; Introduced from Germany by 11th Century St Anselm; Adherent of a Nobleman
COHERENT RING
COHERENT RING
Boy/Male
Tamil
Raghupati | ரகà¯à®ªà®¤à®¿Â
Lord Rama
Boy/Male
Greek
Well born.
Boy/Male
Arabic
Precious
Girl/Female
American, British, Chinese, English, Irish
Clever; Curly-haired
Girl/Female
Biblical
Money, covetousness.
Girl/Female
Indian
Princess
Boy/Male
Israeli
See - a son.
Boy/Male
Tamil
Moon (Lord of night
Surname or Lastname
English (Cornwall)
English (Cornwall) : variant of Sewell.
Boy/Male
Tamil
Muttuk Kumaran | à®®à¯à®¤à¯à®¤à¯à®•Â கà¯à®®à®¾à®°à®¨Â
Lord Murugan
COHERENT RING
COHERENT RING
COHERENT RING
COHERENT RING
COHERENT RING
a.
Adherent part way.
n.
Alt. of Coherency
a.
Incoherent.
p. pr. & vb. n.
of Cohere
a.
Not coherent; wanting cohesion; loose; unconnected; physically disconnected; not fixed to each; -- said of material substances.
a.
Inherent; innate; indwelling.
n.
Coherence of parts.
adv.
In a coherent manner.
imp. & p. p.
of Cohere
a.
Permanently existing in something; inseparably attached or connected; naturally pertaining to; innate; inalienable; as, polarity is an inherent quality of the magnet; the inherent right of men to life, liberty, and protection.
a.
Wanting coherence or agreement; incongruous; inconsistent; having no dependence of one part on another; logically disconnected.
a.
Native; inherent; innate.
a.
Suitable or suited; adapted; accordant.
a.
Sticking together; cleaving; as the parts of bodies; solid or fluid.
a.
Composed of mutually dependent parts; making a logical whole; consistent; as, a coherent plan, argument, or discourse.
n.
Inherence; inherent existence.
a.
Cohering, or sticking together, as in a mass; capable of cohering; tending to cohere; as, cohesive clay.
a.
Intrinsic; inherent; real.
a.
Logically consistent; -- applied to persons; as, a coherent thinker.
n.
The quality or state of being incoherent; want of coherence; want of cohesion or adherence.