On when the multiplicative center of a near-ring is a subnear-ring.
type: Item
instance of: scholarly article
title: On when the multiplicative center of a near-ring is a subnear-ring.
zbMATH Open document ID: 1061.16050
author: Erhard Aichinger
author: Mark Farag
published in: Aequationes Mathematicae
publication date: 2004-11-05T00:00:00Z
review text: Due to the lack of one side of the distributive law, the (multiplicative) center of a nearring may not be a subnearring in general. In this article, the authors investigate when the center of a nearring is itself a subnearring. They first show that a finite simple zero-symmetric nearring \(N\) with nonzero center \(C(N)\) and \(N^2\not=\{0\}\) must have an identity. In this case, if \(C(N)\) is additively closed, then it is a field. In particular, if \(N\) is a von Neumann regular nearring with \(C(N)\) a subnearring, then \(C(N)\) is a commutative von Neumann regular ring, and hence a subdirect product of fields. They continue to describe the multiplicative center of matrix nearrings, and characterize the nearrings with identity of order \(p^2\), \(p\) a prime, that have additively closed center.
reviewed by: Wen-Fong Ke
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2113895
zbMATH Keywords: finite near-rings
zbMATH Keywords: multiplicative centers
zbMATH Keywords: zero-symmetric near-rings
zbMATH Keywords: von Neumann regular near-rings
zbMATH Keywords: matrix near-rings
MaRDI profile type: Publication
full work available at URL: s00010-003-2710-x
OpenAlex ID: W1497068516
DOI: 10.1007/S00010-003-2710-X
description: scientific article; zbMATH DE number 2113895