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in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may alternatively
Dense_submodule
Concept in mathematics
essential submodule is that of superfluous submodule (or small submodule). A submodule N {\displaystyle N} is superfluous if for any other submodule H {\displaystyle
Essential_extension
Topics referred to by the same term
exist in a graph Dense order in order theory A coinitial subset in the mathematical theory of forcing, in set theory Dense submodule in abstract algebra
Density_(disambiguation)
which moreover coincides with the topology induced from A, and that B is dense in A. Picking a generator in each cyclic direct summand of B creates a p-basis
Basic_subgroup
a module is a way to express a module as a direct sum of submodules. dense dense submodule determinant The determinant of a finite free module over a
Glossary_of_module_theory
Algebraic structure
completely reducible) if it is the direct sum of simple (irreducible) submodules. A ring is said to be (left)-semisimple if it is semisimple as a left
Noncommutative_ring
Mathematical theorem in representation theory
U} is a B-submodule if and only if it is invariant under GL ( V ) {\displaystyle \operatorname {GL} (V)} ; in other words, a B-submodule is the same
Schur–Weyl_duality
Mathematical theorem
If u is a non-zero element of U, u • R = U (where u • R is the cyclic submodule of U generated by u). Therefore, if u, v are non-zero elements of U, there
Jacobson_density_theorem
In linear algebra, generated subspace
with the case of vector spaces, the submodule of A spanned by any subset of A is the intersection of all submodules containing that subset. In functional
Linear_span
Nonempty, upper-bounded, downward-closed subset
(mathematics) – Special subset of a partially ordered set Ideal (ring theory) – Submodule of a mathematical ring Ideal on a set – Non-empty family of sets that
Ideal_(order_theory)
Project in integrated circuit design
IP blocks and submodules may be stored and referenced. OpenDB offers a method for adding custom data to objects using sparse or dense attributes. This
OpenROAD_Project
Special subset of a partially ordered set
Cartan 1937b. Bumby, R. T. (1965-12-01). "Modules which are isomorphic to submodules of each other". Archiv der Mathematik. 16 (1): 184–185. doi:10.1007/BF01220018
Filter_(mathematics)
Set whose pairs have minima and maxima
distributive lattices, examples of modular lattices are the lattice of submodules of a module (hence modular), the lattice of two-sided ideals of a ring
Lattice_(order)
Concept in mathematics
dominant weight λ, the irreducible representation L(λ) is the unique simple submodule (the socle) of the Schur module ∇(λ), but it need not be equal to the
Reductive_group
*-algebra of bounded operators on a Hilbert space
ring. Von Neumann algebras are semihereditary: every finitely generated submodule of a projective module is itself projective. There have been several attempts
Von_Neumann_algebra
Device in the representation theory of Lie groups
vector space of finite dimension which is a G-module, its G-submodules and K-submodules are the same.[clarification needed] In the Encyclopedia of Mathematics
Unitarian_trick
Differential variety
{C}}\Omega ^{i}({\mathcal {O}})\subseteq \Omega ({\mathcal {O}})} be the submodule of differential forms over O {\displaystyle {\mathcal {O}}} whose restriction
Diffiety
allows for the module-theoretic terminology: e.g., trivial G-module, G-submodules, etc. G-equivariant vector bundle A G-equivariant vector bundle is a vector
Glossary of representation theory
Glossary_of_representation_theory
Algebraic construct of interest in theoretical physics
of a tensor product of highest weight modules, its decomposition into submodules is the same as for the tensor product of the corresponding modules of
Quantum_group
DENSE SUBMODULE
DENSE SUBMODULE
Girl/Female
American, Australian, French, Greek
Mountain of Zeus; Feminine of Dennis; Follower of Dionysius
Surname or Lastname
English (Kent)
English (Kent) : variant spelling of Denn.
Girl/Female
French
Feminine of Denis from the Greek name Dionysus.
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Indian, Portuguese, Swedish, Swiss
God of Wine; Feminine of Dennis; To Advise; Alone; Nun; Solitary; Follower of Dionysus
Boy/Male
Greek
God of wine.
Boy/Male
English
From the valley.
Girl/Female
Hindu, Indian
People who Give
Girl/Female
American, Australian, British, English, Greek
Combination of Deana and Dina
Boy/Male
Christian, Indian
From Dionysisu; God of Wine
Girl/Female
Indian
Boy/Male
American, Anglo, Australian, British, Christian, English
From the Valley; Place Name; Valley; Occupational Name; Church Official
Girl/Female
Christian & English(British/American/Australian)
Form of Dennis
Girl/Female
Greek
Form of Danae; the mythological mother of Perseus by Zeus.
Girl/Female
English
Combination of Deana (divine) and Dina (from the valley; avenged).
Female
English
Feminine form French Denis, DENISE means "follower of Dionysos."
Surname or Lastname
English
English : ethnic name for someone from Denmark, from Middle English den(s)ch ‘Danish’ (Old English denisc). There were many Danes in England in the Middle Ages, not only the long-established settlers in the Danelaw region, but also more recent immigrants.
Boy/Male
Australian, German, Greek, Hungarian
God of Wine; Wine; Drama; Follower of Dionysus
Girl/Female
English American French
From the Latin Dionysos or Dionysus, referring to the Greek god of wine.
Girl/Female
Australian, Greek
The Mythological Mother of Perseus by Zeus; Form of Danae
Male
English
Variant spelling of English Dean, DENE means "dean, ecclesiastical supervisor."
DENSE SUBMODULE
DENSE SUBMODULE
Boy/Male
Arabic
First Born; Eldest
Surname or Lastname
English
English : unexplained. Possibly an altered form of Isham.
Surname or Lastname
English
English : habitational name from places in Leicestershire and Lincolnshire called Saxby, from the Old Norse personal name Saxi meaning ‘sword’, or the genitive of the Old English folk name Seaxe, Old Norse Saksar ‘Saxons’ + Old Norse býr ‘farm’, ‘settlement’.English : nickname for someone quick to take offense and draw his sword, from Middle English sakespey, Old French sacquespee, from Old French sacque(r) ‘to draw or extract’ (from sac ‘sack’) + espee ‘sword’ (Latin spatha).
Boy/Male
Tamil
Husband of Saraswati
Girl/Female
Anglo Saxon English
Happy.
Girl/Female
Hebrew
Breath.
Girl/Female
British, English, Russian, Turkish
The Sun of the People Nation
Girl/Female
Hindi
Tawny.
Girl/Female
Tamil
Friend
Girl/Female
German
Noble Protector
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
v. t.
Sound perception and reasoning; correct judgment; good mental capacity; understanding; also, that which is sound, true, or reasonable; rational meaning.
v. t.
Moral perception or appreciation.
a.
Having the constituent parts massed or crowded together; close; compact; thick; containing much matter in a small space; heavy; opaque; as, a dense crowd; a dense forest; a dense fog.
v. t.
Meaning; import; signification; as, the true sense of words or phrases; the sense of a remark.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
v. t.
To perfume with odors from burning gums and spices.
v. t.
A faculty, possessed by animals, of perceiving external objects by means of impressions made upon certain organs (sensory or sense organs) of the body, or of perceiving changes in the condition of the body; as, the senses of sight, smell, hearing, taste, and touch. See Muscular sense, under Muscular, and Temperature sense, under Temperature.
v. t.
Perception through the intellect; apprehension; recognition; understanding; discernment; appreciation.
v. t.
One of two opposite directions in which a line, surface, or volume, may be supposed to be described by the motion of a point, line, or surface.
v. t.
To perceive by the senses; to recognize.
n.
A census; -- also, a public rate or tax.
n.
Condition; rank.
n.
One of the forms which a verb takes by inflection or by adding auxiliary words, so as to indicate the time of the action or event signified; the modification which verbs undergo for the indication of time.
v. i.
To burn or scatter incense.
a.
Stupid; gross; crass; as, dense ignorance.
n.
Manliness; dignity; comeliness; civility.
v. t.
Perception by the sensory organs of the body; sensation; sensibility; feeling.
v. t.
To grace.
v. t.
That which is felt or is held as a sentiment, view, or opinion; judgment; notion; opinion.