Matches in SemOpenAlex for { <https://semopenalex.org/work/W2023543645> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W2023543645 endingPage "327" @default.
- W2023543645 startingPage "327" @default.
- W2023543645 abstract "and Fk* the group of units of Fk. Define ring homomorphisms ei (i = 1, , k+ 1) of Fk to Fk+l by(2'3) ei(fl? * ?fk) =fl? * fi?1 fi ... ?fk and define a multiplicative homomorphism Ak: Fk* -> F(k+l)* by Ak(X) = el(x) (E2(X)) * ... (ek+l(x))+1. Then the groups Fk* and mappings Ak form the Amitsur complex; the kth homology group Ker Ak+l/Im Ak we denote by Hk(F). In case F is a finite dimensional extension field, Amitsur showed that H2(F) is isomorphic to the Brauer group of central simple C-algebras split by F. He also showed that in case F is a normal separable extension, Hn(F) is isomorphic to Hn(G, F*) the nth cohomology group of the Galois group G of F over C with coefficients in the group of nonzero elements of F. In this paper, we extend and simplify Amitsur's results. We begin by showing (?2) that in case F is a separable field extension of C, Hn(F) --'Hn([G: H], K*), where K is a normal closure of F with Galois group G, H is the subgroup corresponding to F, and the cohomology group on the right side is the relative cohomology group as introduced in [I]. Next, we study Hn(F) when C is not necessarily a field but when n = 2. In ?3, under weak hypotheses on F, we exhibit a homomorphism of H2(F) to the (generalized) Brauer group of central separable algebra classes split by F [5]. This homomorphism is an isomorphism under stronger hypotheses on F and C. These hypotheses are slightly weaker than assuming all projective C, F, and F2 modules are free and include the cases (10) C is semilocal (not necessarily Noetherian) and F is a C-algebra which is a-finitely generated projective C-module containing C 1 as a direct summand and (20) C=K[x], F=L[x], with K a field and L a finite dimensional commutative K-algebra. Hochschild in [13] has given a description of the Brauer group in case F is a purely inseparable extension field of C of exponent 1. In [3, ?7], Amitsur" @default.
- W2023543645 created "2016-06-24" @default.
- W2023543645 creator A5013027949 @default.
- W2023543645 creator A5065460711 @default.
- W2023543645 date "1960-02-01" @default.
- W2023543645 modified "2023-09-26" @default.
- W2023543645 title "On Amitsur’s complex" @default.
- W2023543645 cites W1505271990 @default.
- W2023543645 cites W1602931685 @default.
- W2023543645 cites W1767722407 @default.
- W2023543645 cites W1977394356 @default.
- W2023543645 cites W1979277521 @default.
- W2023543645 cites W1986872508 @default.
- W2023543645 cites W2012874740 @default.
- W2023543645 cites W2041570432 @default.
- W2023543645 cites W2050151425 @default.
- W2023543645 cites W2090504196 @default.
- W2023543645 cites W2253806737 @default.
- W2023543645 cites W2313857119 @default.
- W2023543645 cites W2315944763 @default.
- W2023543645 cites W2316605989 @default.
- W2023543645 doi "https://doi.org/10.1090/s0002-9947-1960-0121391-4" @default.
- W2023543645 hasPublicationYear "1960" @default.
- W2023543645 type Work @default.
- W2023543645 sameAs 2023543645 @default.
- W2023543645 citedByCount "19" @default.
- W2023543645 countsByYear W20235436452016 @default.
- W2023543645 countsByYear W20235436452019 @default.
- W2023543645 crossrefType "journal-article" @default.
- W2023543645 hasAuthorship W2023543645A5013027949 @default.
- W2023543645 hasAuthorship W2023543645A5065460711 @default.
- W2023543645 hasBestOaLocation W20235436451 @default.
- W2023543645 hasConcept C202444582 @default.
- W2023543645 hasConcept C33923547 @default.
- W2023543645 hasConceptScore W2023543645C202444582 @default.
- W2023543645 hasConceptScore W2023543645C33923547 @default.
- W2023543645 hasIssue "2" @default.
- W2023543645 hasLocation W20235436451 @default.
- W2023543645 hasOpenAccess W2023543645 @default.
- W2023543645 hasPrimaryLocation W20235436451 @default.
- W2023543645 hasRelatedWork W1557945163 @default.
- W2023543645 hasRelatedWork W1985218657 @default.
- W2023543645 hasRelatedWork W2023661790 @default.
- W2023543645 hasRelatedWork W2073994398 @default.
- W2023543645 hasRelatedWork W2096753949 @default.
- W2023543645 hasRelatedWork W2963341196 @default.
- W2023543645 hasRelatedWork W3106133691 @default.
- W2023543645 hasRelatedWork W3124205579 @default.
- W2023543645 hasRelatedWork W3134646037 @default.
- W2023543645 hasRelatedWork W4249580765 @default.
- W2023543645 hasVolume "97" @default.
- W2023543645 isParatext "false" @default.
- W2023543645 isRetracted "false" @default.
- W2023543645 magId "2023543645" @default.
- W2023543645 workType "article" @default.