On the cohomology of Frobenius algebras
type: Item
instance of: scholarly article
title: On the cohomology of Frobenius algebras
zbMATH Open document ID: 0808.16013
DOI: 10.1016/0022-4049(92)90070-V
author: Katsunori Sanada
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: Let \(\Lambda\) be a finitely generated free Frobenius algebra over a commutative ring \(R\). The author investigates the complete cohomology groups \(H^ \tau (\Lambda, -)\) [\textit{T. Nakayama}, Osaka Math. J. 9, 165-187 (1957; Zbl 0101.02601)], in particular their periodicity with respect to \(r\). Then, applications to the cohomology of the rings of integers in quadratic fields over the rationals \(\mathbb{Q}\) are presented.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 89574
zbMATH Keywords: cohomology rings
zbMATH Keywords: finitely generated free Frobenius algebra
zbMATH Keywords: complete cohomology groups
zbMATH Keywords: periodicity
zbMATH Keywords: quadratic fields
Wikidata QID: Q112879907
reviewed by: Marek Golasiński
MaRDI profile type: Publication
cites work: The Brauer Group of a Commutative Ring
cites work: Q4143495
cites work: Q3240881
cites work: Q3282976
cites work: Q5587110
description: scientific article; zbMATH DE number 89574