On ideal and subalgebra coefficients in semigroup algebras
type: Item
instance of: scholarly article
title: On ideal and subalgebra coefficients in semigroup algebras
zbMATH Open document ID: 0984.20045
DOI: 10.1007/BF03322683
author: Rainer Steinwandt
published in: Results in Mathematics
publication date: 2002-02-19T00:00:00Z
review text: Let \(k\) be a field, let \(S\) be a semigroup, and let \(k[S]\) be the semigroup ring of \(S\) over \(k\). Suppose \(U\) is either a one-sided ideal of \(k[S]\) or else a \(k\)-subalgebra of \(k[S]\). It is shown that there exists a smallest subfield \(k'\) of \(k\) such that \(U\) is generated by elements of \(k'[S]\). If one takes \(S\) a free commutative semigroup, the theorem above becomes a well known fact from the theory of polynomial rings over fields. The author constructs an example showing that a semigroup ring cannot be changed to a general commutative algebra over a field.
reviewed by: Josif S. Ponizovskii
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 1618954
zbMATH Keywords: fields of definition
zbMATH Keywords: subalgebras
zbMATH Keywords: semigroup rings
zbMATH Keywords: one-sided ideals
MaRDI profile type: Publication
cites work: Q5846813
cites work: Q3272926
cites work: Ideal and subalgebra coefficients
cites work: Q4232490
cites work: Q3156428
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description: scientific article; zbMATH DE number 1618954