Spectral sequence for MacLane homology
type: Item
instance of: scholarly article
title: Spectral sequence for MacLane homology
zbMATH Open document ID: 0811.18009
author: Teimuraz Pirashvili
published in: Journal of Algebra
publication date: 1994-12-19T00:00:00Z
review text: \textit{S. MacLane} has defined the cohomology of a ring \(R\) with coefficients in an \(R\)-\(R\)-bimodule \(M\) based on the Hochschild cohomology of a chain algebra which has the same homology as the Eilenberg-MacLane spectrum [Colloq. Topologie algébrique, Louvain, 1956, 55-80 (1957; Zbl 0084.267)]. Dually one has the MacLane homology. This one and the Hochschild homology are related by a spectral sequence [see the author and \textit{F. Waldhausen}, J. Pure Appl. Algebra 82, No. 1, 81-98 (1992; Zbl 0767.55010)]. In the present paper it is proved that if \(R\) is a monoid ring or a smooth algebra, then the differentials of the spectral sequence are zero. That is also true for algebras over \(\mathbb{F}_ p\) where \(p\) is a prime.
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 18G40
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 703227
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: MacLane homology
zbMATH Keywords: Hochschild homology
zbMATH Keywords: spectral sequence
reviewed by: Georges Hoff
MaRDI profile type: Publication
full work available at URL: jabr.1994.1345
OpenAlex ID: W1984764167
DOI: 10.1006/JABR.1994.1345
description: scientific article; zbMATH DE number 703227