Dual coalgebras of algebras over commutative rings
type: Item
instance of: scholarly article
title: Dual coalgebras of algebras over commutative rings
zbMATH Open document ID: 0980.16030
DOI: 10.1016/S0022-4049(99)00088-2
author: Jawad Abuhlail
author: José Gómez-Torrecillas
author: Robert Wisbauer
published in: Journal of Pure and Applied Algebra
publication date: 2001-02-05T00:00:00Z
review text: Let \(R\) be a Noetherian ring and let \(A\) be an \(R\)-algebra, considered as a multiplicative monoid. The finite dual \(A^\circ\) is defined as the \(R\)-submodule of \(R^A\) consisting of \(R\)-valued representative functions on \(A\). The main result of this paper states that \(A^\circ\) is an \(R\)-coalgebra, provided that \(A^\circ\subseteq R^A\) is a pure \(R\)-submodule. This last condition is satisfied if \(R\) is a Noetherian hereditary ring. This result is applied by the two first authors and \textit{F. J. Lobillo} in their paper [J. Algebra 240, No. 1, 165-184 (2001; see the preceding review Zbl 0980.16028)]. A related result, for the case where \(R\) is a Dedekind domain, appears in the paper [Commun. Algebra 18, No. 10, 3209-3221 (1990; Zbl 0742.16018)] by \textit{C. Chen} and \textit{W. D. Nichols}.
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 1538660
zbMATH Keywords: representative functions
zbMATH Keywords: dual coalgebras
zbMATH Keywords: monoid algebras
MaRDI profile type: Publication
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Wikidata QID: Q127191059
description: scientific article; zbMATH DE number 1538660