On the cohomology of ring extensions
type: Item
instance of: scholarly article
title: On the cohomology of ring extensions
zbMATH Open document ID: 0734.16003
DOI: 10.1016/0001-8708(91)90061-B
author: Rolf Farnsteiner
published in: Advances in Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Here the author is primarily concerned with the relativized cohomology theory of ring extensions as initiated by G. Hochschild. The approach chosen here heavily emphasizes the role of locally nilpotent operators. Various vanishing theorems for extension functors are obtained. Applications to the cohomology theory of modular Lie algebras and ring theory are illustrated.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 16S70
zbMATH DE Number: 4214213
zbMATH Keywords: Frobenius extension
zbMATH Keywords: cohomology
zbMATH Keywords: ring extensions
zbMATH Keywords: locally nilpotent operators
zbMATH Keywords: vanishing theorems
zbMATH Keywords: extension functors
zbMATH Keywords: modular Lie algebras
reviewed by: Guangyu Shen
MaRDI profile type: Publication
cites work: Q4056148
cites work: Q3240881
cites work: Cohomology Theory of Lie Groups and Lie Algebras
cites work: Relative Homological Algebra and Homological Dimension of Lie Algebras
cites work: On the Vanishing of Homology and Cohomology Groups of Associative Algebras
cites work: Q3822337
cites work: Q3995365
cites work: Extension functors of modular Lie algebras
cites work: Shapiro's lemma and its consequences in the cohomology theory of modular Lie algebras
cites work: Q4729952
cites work: Q5648522
cites work: On Relative Homological Algebra of Frobenius Extensions
cites work: Representations of Restricted Lie Algebras of Characteristic p
cites work: Relative Homological Algebra
cites work: Note on Relative Homological Dimension
cites work: Dualitätseigenschaften von Frobenius-Erweiterungen
cites work: An Associative Orthogonal Bilinear Form for Hopf Algebras
cites work: On Frobenius Extensions I.
cites work: On Frobenius Extensions II
cites work: Einige Bemerkungen über Frobenius-Erweiterungen
cites work: When Hopf algebras are Frobenius algebras
cites work: On the cohomology of modules over Hopf algebras
cites work: Q3882615
cites work: Q4039778
cites work: Integrals for Hopf algebras
full work available at URL: 0001-8708(91)90061-b
OpenAlex ID: W2013824808
description: scientific article; zbMATH DE number 4214213