The isomorphism problem for commutative monoid rings
type: Item
instance of: scholarly article
title: The isomorphism problem for commutative monoid rings
zbMATH Open document ID: 0931.20053
DOI: 10.1016/S0022-4049(97)00063-7
author: Joseph Gubeladze
published in: Journal of Pure and Applied Algebra
publication date: 2000-02-28T00:00:00Z
review text: The isomorphism problem for monoid rings asks whether two monoids are isomorphic if they have isomorphic monoid rings. Here all monoids are commutative, cancellative, and torsionfree and all rings are commutative with 1. The main result of this paper is that if \(M\) and \(N\) are finitely generated monoids and \(R\) is a ring with \(R[M]\approx R[N]\) as \(R\)-algebras, then \(M\approx N\) if either (1) \(M\) is normal, (2) \(M\) and \(N\) have only trivial units and \(R[M]\approx R[N]\) as augmented \(R\)-algebras, or (3) \(M\) is homogeneous. The proof is accomplished by extending and correcting arguments in a paper of \textit{A. S. Demushkin} [Vestn. Mosk. Univ., Ser. I 1982, No. 2, 80-87 (1982; Zbl 0507.14033)]. As an application, the author also gives a positive answer to the isomorphism problem for discrete Hodge algebras.
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 13L05
zbMATH DE Number: 1308187
zbMATH Keywords: isomorphism problem
zbMATH Keywords: monoid rings
zbMATH Keywords: finitely generated monoids
zbMATH Keywords: discrete Hodge algebras
reviewed by: David F. Anderson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308187