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Near-rings with chain conditions on right annihilators

Published online by Cambridge University Press:  20 January 2009

A. Oswald
A. Oswald
Affiliation:
Department of Mathematics and StatisticsTeesside PolytechnicMiddlesbroughCleveland
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Throughout this note, N will denote a (Left) near-ring with two-sided zero. Definitions of basic concepts can be found in (9).

We prove first that a right ideal I in a d.g. near-ring has a right identity if and only if x ∈ xI for each x ∈I. This enables us to study the structure of regular d.g. near-rings with chain conditions on right annihilators. Specifically we will prove that a regular d.g. near-ring with both the maximum and the minimum conditions on right annihilators is a finite direct sum of near-rings which are either rings of matrices over division rings or non-rings of the form MG(Γ) for a suitable type 2 N-module Γ. Finally we consider the case of maximum condition on N-subgroups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 1 , February 1980 , pp. 123 - 127
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

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