Hochschild cohomology rings of algebras \(k[X]/(f)\)
type: Item
instance of: scholarly article
title: Hochschild cohomology rings of algebras \(k[X]/(f)\)
zbMATH Open document ID: 0961.13006
author: Thorsten Holm
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-05-03T00:00:00Z
full work available at URL: https://eudml.org/doc/231514
full work available at URL: BAG
review text: Let \(k\) be a commutative ring, \(f\in k[X]\) a monic polynomial. The author investigates the structure of the Hochschild cohomology ring for the \(k\)-algebra \(k[X]/(f)=A_f\). The subring of classes of even degree depends very precisely on the ring structure of \(A_f\). For the full cohomology ring particularly the situation is studied, where \(f\) is a power of an irreducible separable polynomial or \(f=X^n\). The latter case contains modular group algebras of cyclic \(p\)-groups and, therefore, generalises earlier results [\textit{Th. Holm}, Commun. Algebra 24, No. 6, 1957-1969 (1996; Zbl 0853.16016)].
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 1428680
zbMATH Keywords: projective resolution
zbMATH Keywords: Hochschild cohomology ring
zbMATH Keywords: modular group algebras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1428680