The \(J_ 0\)-radical of matrix near-rings
type: Item
instance of: scholarly article
title: The \(J_ 0\)-radical of matrix near-rings
zbMATH Open document ID: 0728.16025
DOI: 10.1007/BF01200344
author: N. E. Zubov
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: The main result is: Let \((R,+,.)\) be a weakly distributive d.g. right near-ring with identity. Then \(J_ 0(R)^*=J_ 0(M_ n(R))\). Notation: if \(R^ n\) is the direct sum of n copies of \((R,+)\), let \(M(R^ n)\) be the near-ring of all mappings of the group \(R^ n\) into itself (under pointwise addition and composition of mappings); \(M_ n(R)\) is then defined to be the subnear-ring of \(M(R^ n)\) generated by the set of all mappings \(\iota_ i\lambda (r)\pi_ j\), where \(r\in R\), \(1\leq i,j\leq n\), \(\lambda\) (r): \(R\to R\) is left multiplication by r, \(\pi_ j\) is the j-th coordinate projection \(R^ n\to R\), and \(\iota_ i\) is the i-th coordinate injection \(R\to R^ n\); for a near-ring R, the authors define \(J_ 0(R)\) to be the intersection of all annihilators of monogenic simple (left) R-modules; for an ideal I of R, they define \(I^*=\{A\in M_ n(R)\); \(AR^ n\subseteq I^ n\}\).
reviewed by: Hans Lausch
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16N20
zbMATH DE Number: 4202518
zbMATH Keywords: near-ring of mappings
zbMATH Keywords: weakly distributive d.g. right near-ring
MaRDI profile type: Publication
cites work: Q3807388
cites work: Matrix near rings
cites work: Q3941589
cites work: PRIMITIVITY IN MATRIX NEAR-RINGS
full work available at URL: https://doi.org/10.1007/bf01200344
OpenAlex ID: W2064642167
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description: scientific article; zbMATH DE number 4202518