A field-like property of finite rings
type: Item
instance of: scholarly article
title: A field-like property of finite rings
zbMATH Open document ID: 0771.16009
DOI: 10.1016/0019-3577(92)90024-F
author: H. L. Claasen
author: R. W. Goldbach
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: Let \(R\) be a finite ring and \(R^ +\) its additive group. The group \(\Omega\) of characters of \(R^ +\) is an \(R\)-bimodule with operators defined by \((a\omega b)(x) = \omega(bxa)\), \(\omega \in \Omega\), \(a,b,x \in R\). The authors call the ring \(R\) left (right) admissible if \(\Omega\) is isomorphic to \(R^ +\) as a right (left) \(R\)-module. The admissibility of finite rings, called their field-like property in the paper, is investigated for rings with a few minimal one-sided ideals, for semi- simple, local and commutative rings. In particular, the relation between the admissibility and the structure of the one-sided socle of \(R\) is considered and general necessary and sufficient conditions of the admissibility are established.
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 13M05
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 16L30
zbMATH DE Number: 57228
zbMATH Keywords: additive group
zbMATH Keywords: admissibility of finite rings
zbMATH Keywords: minimal one-sided ideals
zbMATH Keywords: commutative rings
reviewed by: Feliks R. Bobovich
MaRDI profile type: Publication
cites work: Cyclotomic schemes over finite rings
cites work: Q3236717
cites work: Q4046212
full work available at URL: 0019-3577(92)90024-f
OpenAlex ID: W1987424956
description: scientific article; zbMATH DE number 57228