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In algebra, the Amitsur complex is a natural complex associated to a ring homomorphism. It was introduced by Shimshon Amitsur (1959). When the homomorphism
Amitsur_complex
Israeli mathematician (1921–1994)
Shimshon Avraham Amitsur (born Kaplan; Hebrew: שמשון אברהם עמיצור; August 26, 1921 – September 5, 1994) was an Israeli mathematician. A leading figure
Shimshon_Amitsur
Tool in homological algebra
C))} Amitsur complex A complex used to define Bloch's higher Chow groups Buchsbaum–Rim complex Čech complex Cousin complex Eagon–Northcott complex Gersten
Chain_complex
Construct in algebraic geometry
cosimplicial object determining the Amitsur complex.) More generally, all the exterior powers of the cotangent complex satisfy faithfully flat descent. Let
Cotangent_complex
Algebraic structure in ring theory
A → B , {\displaystyle f:A\to B,} there is an associated complex called the Amitsur complex: 0 → A → f B → δ 0 B ⊗ A B → δ 1 B ⊗ A B ⊗ A B → ⋯ {\displaystyle
Flat_module
Bhatt & Scholze (2019, §8) show that the Amitsur complex of an arc covering of perfect rings is an exact complex. List of topologies on the category of
V-topology
Technique from algebraic geometry
row is exact by the flatness of B over A and the bottom row is the Amitsur complex, which is exact by a theorem of Grothendieck. The cocycle condition
Faithfully_flat_descent
S T U V W XYZ See also References Amitsur complex The Amitsur complex of a ring homomorphism is a cochain complex that measures the extent in which the
Glossary_of_ring_theory
Hochschild complex of A over B with coefficients in A, and cup product, is isomorphic as differential graded algebras to the Amitsur complex of the R-coring
Depth of noncommutative subrings
Depth_of_noncommutative_subrings
theorem (algebraic geometry) Zariski's main theorem (algebraic geometry) Amitsur–Levitzki theorem (linear algebra) Binomial inverse theorem (linear algebra)
List_of_theorems
Israeli mathematician
Jerusalem. His master thesis was done under the supervision of Shimshon Amitsur. He received his Ph.D. from the Massachusetts Institute of Technology in
Amnon_Yekutieli
u-invariant 6 after A. Merkurjev". Ring theory 1989. In honor of S. A. Amitsur, Proc. Symp. and Workshop, Jerusalem 1988/89. Israel Math. Conf. Proc.
U-invariant
for infinite graphs by Ron Aharoni. Development of the Amitsur–Levitzki theorem by Shimshon Amitsur. The Benjamini-Hochberg procedure for controlling the
List of Israeli inventions and discoveries
List_of_Israeli_inventions_and_discoveries
lemma); Abraham Fraenkel (Zermelo–Fraenkel set theory); Shimshon Amitsur(Amitsur–Levitzki theorem); Saharon Shelah (Sauer–Shelah lemma); Elon Lindenstrauss
Culture_of_Israel
(2000) Franz Alt (1910–2011), mathematician and computer scientist Shimshon Amitsur (1921–1994), mathematician Jacob Anatoli (c. 1194–1256), mathematician
List_of_Jewish_mathematicians
Israeli mathematician of Latvian origin (1948–2024)
Vietoris–Rips complex Torah Code Awards Erdős Prize (1979) Scientific career Fields Mathematics Institutions Hebrew University Doctoral advisor Shimshon Amitsur Doctoral
Eliyahu_Rips
Bilateral relations
until 24 hours after the assassination, and according to Israeli historian Amitsur Ilan, the investigation was "amateurish." It was not until 1995 that Shimon
Israel–Sweden_relations
AMITSUR COMPLEX
AMITSUR COMPLEX
Surname or Lastname
English
English : from the popular medieval personal name Hudde, which is of complex origin. It is usually explained as a pet form of Hugh, but there was a pre-existing Old English personal name, Hūda, underlying place names such as Huddington, Worcestershire. This personal name may well still have been in use at the time of the Norman Conquest. If so, it was absorbed by the Norman Hugh and its many diminutives. Reaney adduces evidence that Hudde was also regarded as a pet form of Richard.German : from a short form of a Germanic compound personal name formed with hut ‘guard’ as the first element.Variant spelling of German Hütt (see Huett).Jewish (Ashkenazic) : metonymic occupational name from Yiddish hut, German Hut ‘hat’ (see Huth).
Boy/Male
Arabic, Muslim
Easy; Successful; Fortunate; Lucky; Prosperous
Surname or Lastname
English (Midlands)
English (Midlands) : nickname for a dark-complexioned man, from Old English earp ‘swarthy’.Americanized spelling of German Erp.
Surname or Lastname
German
German : nickname from the small medieval coin known as the häller or heller because it was first minted (in 1208) at the Swabian town of (Schwäbisch) Hall. Compare Hall.Jewish (Ashkenazic) : habitational name for someone from Schwäbisch Hall.German : topographic name for someone living by a field named as ‘hell’ (see Helle 3).English : topographic name for someone living on a hill, from southeastern Middle English hell + the habitational suffix -er.Dutch : from a Germanic personal name composed of the elements hild ‘strife’ + hari, heri ‘army’.Jewish (Ashkenazic) : nickname for a person with fair hair or a light complexion, from an inflected form, used before a male personal name, of German hell ‘light’, ‘bright’, Yiddish hel.
Girl/Female
Japanese
Surname meaning shine; reflect.
Girl/Female
English
Honey; Light
Surname or Lastname
English
English : occupational name for a fiddle player or a nickname for a skilled or enthusiastic amateur, from Old English fiðelere ‘fiddler’.German : variant of Fiedler.
Boy/Male
Muslim
Easy, Successful, Fortunate
Boy/Male
Indian
Easy, Successful, Fortunate
Surname or Lastname
English
English : variant of Grice.French (Grisé) : variant spelling of Griset, a nickname for someone with gray hair, a gray complexion, or perhaps one who habitually wore gray, from Old French gris ‘gray’.
Surname or Lastname
English
English : nickname from Middle English gulle ‘gull’ or gul(le) (Old Norse gulr) ‘yellow’, ‘pale’ (of hair or complexion).Swiss German : nickname for an irascible or unreliable person, from an Alemannic form of Latin gallus ‘rooster’. See also Guell.
Surname or Lastname
Irish
Irish : reduced Anglicized form of Gaelic Ó Duinn, Ó Doinn ‘descendant of Donn’, a byname meaning ‘brown-haired’ or ‘chieftain’.English : nickname for a man with dark hair or a swarthy complexion, from Middle English dunn ‘dark-colored’.Scottish : habitational name from Dun in Angus, named with Gaelic dùn ‘fort’.Scottish : nickname from Gaelic donn ‘brown’. Compare 1.
Boy/Male
Indian, Punjabi, Sikh
Unlimited Bravery
Surname or Lastname
English
English : nickname for someone with a complexion that was as ‘white as a lily’ (Middle English lilie).
Surname or Lastname
English
English : nickname for a person with a ruddy complexion, from an adjective derivative of Middle English mad(d)er ‘madder’, the dye plant (see Mader 1), here used in a transferred sense.
Male
Japanese
(å…‰å) Japanese name MITSUO means "shining man."
Girl/Female
Tamil
Gourangi | கௌராஂகீ
Giver of happiness, One name of radhas name, Lord krishnas beloved, Fair complexioned
Gourangi | கௌராஂகீ
Boy/Male
Hindu, Indian
An Entry Point into a Dispute
Female
Japanese
(満) Japanese unisex name MITSURU means "full" or "growing."
Surname or Lastname
English
English : from Old English dūst ‘dust’, applied as a nickname, possibly for someone with a dusty complexion or hair (as, for example, a miller), or for a worthless person.North German : possibly a Westphalian habitational name from a farm named with dost ‘bush’, ‘brush’. However, the word also means ‘fine dust’, ‘flour’ and may have been applied as an occupational nickname for a miller. Compare 1.
AMITSUR COMPLEX
AMITSUR COMPLEX
Girl/Female
Tamil
Girl/Female
Gujarati, Hindu, Indian
Decorative Star / Sitara
Girl/Female
Muslim
Little, Light rain, Drizzle, Mercy
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
One with Pure Heart; Very Kind; Loving
Girl/Female
Arabic, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Telugu
Love
Girl/Female
Arabic, Muslim
Most Prosperous
Girl/Female
American, Australian, Danish, French, German, Hebrew, Swiss
God is My Judge; Female Version of Daniel
Biblical
essence; being; generation
Boy/Male
Australian, German, Italian
Victorious; Conquerer of the People
Boy/Male
Afghan, Arabic, Hindu, Indian, Muslim, Sanskrit
The God of Death; Also the Five Moral Commandments
AMITSUR COMPLEX
AMITSUR COMPLEX
AMITSUR COMPLEX
AMITSUR COMPLEX
AMITSUR COMPLEX
a.
Having (such) a complexion; -- used in composition; as, a dark-complexioned or a ruddy-complexioned person.
n.
The general appearance or aspect; as, the complexion of the sky; the complexion of the news.
a.
Pertaining to the complexion, or to the care of it.
n.
The state of being complex; complexity.
a.
Engaged in by professionals; as, a professional race; -- opposed to amateur.
n.
A person attached to a particular pursuit, study, or science as to music or painting; esp. one who cultivates any study or art, from taste or attachment, without pursuing it professionally.
n.
That which is complex; intricacy; complication.
v. t.
An admirer or lover of the fine arts; popularly, an amateur; especially, one who follows an art or a branch of knowledge, desultorily, or for amusement only.
n.
The practice, habit, or work of an amateur.
n.
The quality or character of an amateur.
n.
An amateur collector and breeder of insects, esp. of butterflies and moths; a lepidopterist.
n.
The state of being complex; intricacy; entanglement.
n.
A person who prosecutes anything professionally, or for a livelihood, and not in the character of an amateur; a professional worker.
n.
A complex; an aggregate of parts; a complication.
a.
Of or pertaining to constitutional complexion.
a.
Of or pertaining to dilettanteism; amateur; as, dilettant speculation.
a.
Of or pertaining to an amateur sailor or yachtsman; as, a corinthian race (one in which the contesting yachts must be manned by amateurs.)
pl.
of Complexity
a.
In the style of an amateur; superficial or defective like the work of an amateur.
adv.
In a complex manner; not simply.