Matrix near-rings and 0-primitivity

Wen-Fong Ke, J. H. Meyer

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Abstract

In this article, we study the implication of the primitivity of a matrix near-ring M n (R) (n > 1) and that of the underlying base near-ring R. We show that when R is a zero-symmetric near-ring with identity and M n(R)has the descending chain condition on M n(R)-subgroups, then the 0-primitivity of M n(R)implies the 0-primitivity of R. It is not known if this is true when the descending chain condition on M n(R)is removed. On the other hand, an example is given to show that this is not true in the case of generalized matrix near-rings.

Original languageEnglish
Pages (from-to)353-363
Number of pages11
JournalMonatshefte fur Mathematik
Volume165
Issue number3-4
DOIs
Publication statusPublished - 2012 Mar 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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