Strongly monogenic near-rings
type: Item
instance of: scholarly article
title: Strongly monogenic near-rings
zbMATH Open document ID: 0629.16019
DOI: 10.1007/BF01198634
author: Raffaele Scapellato
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let N be a left zero-symmetric near-ring. N is said to be strongly monogenic (s.m.) if aN\(\in \{0,N\}\) for all \(a\in N\) and \(bN=N\) for some \(b\in N\). N is said to be geometric if for each a,b\(\in N\) there is an \(e\in N\) such that \(ea=a\) and if ab\(\neq 0\) then \(Nab=Nb\). It is shown that an s.m. near-ring N has a unique maximal ideal R, equal to the Jacobson-type radical \(J_ 1(N)\) and to the prime radical P(N). Moreover \(J_ 2(N)\) is equal either to R or to N. Some characterizations of near- rings that are both s.m. and geometric are also given.
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16Nxx
zbMATH DE Number: 4023514
zbMATH Keywords: left zero-symmetric near-ring
zbMATH Keywords: strongly monogenic
zbMATH Keywords: geometric
zbMATH Keywords: maximal ideal
zbMATH Keywords: prime radical
zbMATH Keywords: Jacobson-type radical
MaRDI profile type: Publication
cites work: Q4119339
cites work: Q3671335
cites work: Q3318922
cites work: Q3715279
description: scientific article; zbMATH DE number 4023514