Wedderburn-Artin theorem analogue for near-rings.
type: Item
instance of: scholarly article
title: Wedderburn-Artin theorem analogue for near-rings.
zbMATH Open document ID: 1086.16030
author: Ravi Srinivasa Rao
published in: Southeast Asian Bulletin of Mathematics
publication date: 2004-11-25T00:00:00Z
review text: The author considers only zero symmetric right near-rings with identity. He uses right ideals to obtain an analogue of the Wedderburn-Artin Theorem for rings. So a right completely reducible near-ring \(R\) is one which is a direct sum of strictly minimal right ideals (that is right ideals generated as right \(R\)-groups by any one non-zero element). Then he shows that a right completely reducible near-ring \(R\) with isomorphic strictly minimal right ideals is a simple near-ring containing a matrix near-ring over a near-field, and, if finite, is isomorphic to a matrix near-ring over a near-field if \(eRe\) is not a division ring for a strictly minimal right ideal \(eR\), \(e\) a distributive idempotent in \(R\). Also a near-ring is right completely reducible if and only if it is isomorphic to a finite direct product of right completely reducible simple near-rings. A simple near-ring is constructed which is the direct sum of two non-right-\(R\)-isomorphic minimal right ideals. Much use is made of the author's earlier paper [Quaest. Math. 17, No. 3, 321-332 (1994; Zbl 0818.16034)].
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D60
zbMATH DE Number: 2119032
zbMATH Keywords: zero-symmetric right near-rings
zbMATH Keywords: completely reducible near-rings
zbMATH Keywords: simple near-rings
zbMATH Keywords: matrix near-rings
zbMATH Keywords: strictly minimal right ideals
reviewed by: John D. P. Meldrum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2119032