Cohomology and extensions of inverse semigroups
type: Item
instance of: scholarly article
title: Cohomology and extensions of inverse semigroups
zbMATH Open document ID: 0358.20076
DOI: 10.1016/0021-8693(77)90206-X
author: S. Sribala
published in: Journal of Algebra
publication date: 1977-01-01T00:00:00Z
review text: The concept of idempotent separating extensions of inverse semigroups was studied by \textit{D'Alarco} and a cohomological Interpretation was given by \textit{Lausch}. Our definition of extension is a particular case of \textit{D'Alarco's} definition. In this paper, we define \(\theta\)-extension of a semilattice of abelian groups \(A\) by a semilattice of groups \(B\) and we introduce a multiplication in the set \(\mathrm{Ext}(B,A)\) of equivalence classes of \(\theta\)-extensions of \(A\) by \(B\), similar to the Baer multiplication in the case of group extensions. We show that \(\mathrm{Ext}(B,A)\) is an abelian group and study the functional properties of \(\mathrm{Ext}(+ , -)\). We prove that \(\mathrm{Ext}(B,A)\) and \(H_{B^{2}}^{2}(A^{0})\) are naturally isomorphic.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M99
zbMATH DE Number: 3558114
MaRDI profile type: Publication
cites work: Q3848243
cites work: Idempotent-Separating Extensions Of Inverse Semigroups
cites work: Cohomology theory in abstract groups. I
cites work: Semigroup Extensions.
cites work: Cohomology of inverse semigroups
cites work: Q5343374
full work available at URL: 0021-8693(77)90206-x
OpenAlex ID: W2083801632
description: scientific article; zbMATH DE number 3558114