Rings which are sums of finite fields
type: Item
instance of: scholarly article
title: Rings which are sums of finite fields
zbMATH Open document ID: 0924.16021
published in: Finite Fields and their Applications
publication date: 1999-10-31T00:00:00Z
review text: It is shown that a semigroup ring \(R[S]\) is a direct sum of finite fields if and only if \(R\) is a ring of this type, \(S\) is a commutative semigroup in which every principal ideal is finite and \(S\) is torsion-disjoint with \(R\) (that is, \(s^n=t^n\) for \(s,t\in S\), \(s\neq t\), implies that \(R\) has no \(n\)-torsion). A characterization of rings that are direct sums of finite fields is also obtained for a certain class of rings graded by a semilattice. Finally, if \(\mathcal K\) is the class of rings that are sums of finite fields and a finite commutative ring \(R\) is a sum of its subrings \(R_i\in{\mathcal K}\), \(i=1,\dots,n\), then \(R\in{\mathcal K}\).
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 13M05
zbMATH DE Number: 1271779
zbMATH Keywords: graded rings
zbMATH Keywords: semigroup rings
zbMATH Keywords: direct sums of finite fields
zbMATH Keywords: commutative semigroups
zbMATH Keywords: principal ideals
zbMATH Keywords: finite commutative rings
author: A. V. Kelarev
reviewed by: Jan Okniński
MaRDI profile type: Publication
full work available at URL: ffta.1998.0240
OpenAlex ID: W2056386790
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DOI: 10.1006/FFTA.1998.0240
description: scientific article; zbMATH DE number 1271779