Nilpotent extensions and some associated invariants
type: Item
instance of: scholarly article
title: Nilpotent extensions and some associated invariants
zbMATH Open document ID: 0863.18008
author: Shmuel Rosset
published in: Journal of Algebra
publication date: 1996-06-10T00:00:00Z
review text: The paper is concerned with certain (Schur-)Baer-(Fröhlich-)invariants associated with an augmented algebra \(A\) over the commutative ring \(k\). The corresponding functors are defined by means of nilpotent extensions. The author deduces a five term exact sequence involving some of these invariants, which generalizes the well-known five term sequence in low degrees in the homology theory of groups. (The Baer-invariants considered here and the corresponding sequence have also been obtained -- in very general circumstances including the two cases mentioned above -- by \textit{J. Furtado-Coelho} [J. Algebra 40, 596-609 (1976; Zbl 0372.20037)].) A new proof is given that one of the introduced Baer-invariants can be interpreted using homological algebra as \(\text{Tor}^A_2 (k,k)\). Various results are then deduced from the corresponding five term exact sequence; this sequence -- again in a more general form -- can be found in a paper by \textit{M.-A. Knus} [J. Algebra 9, 274-284 (1968; Zbl 0162.05103)] together with most of the consequences obtained by the author of the present paper.
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 868031
zbMATH Keywords: universal extensions
zbMATH Keywords: Tor
zbMATH Keywords: augmented algebra
zbMATH Keywords: nilpotent extensions
zbMATH Keywords: homology theory of groups
zbMATH Keywords: Baer-invariants
zbMATH Keywords: five term exact sequence
reviewed by: Urs Stammbach
MaRDI profile type: Publication
full work available at URL: jabr.1996.0047
OpenAlex ID: W1974584112
DOI: 10.1006/JABR.1996.0047
description: scientific article; zbMATH DE number 868031