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Near-Ring Homomorphisms

Published online by Cambridge University Press:  20 November 2018

Joseph J. Malone Jr
Joseph J. Malone Jr*
Affiliation:
Texas A and M University
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Blackett [4] introduced the concepts of near-ring homomorphism and near-ring ideal. Beidleman [1] established the fundamental homomorphism theorem and the isomorphism theorems for (left) near - rings obeying the condition that 0.a = 0 for every a in the near-ring. Several others, for example [3], [5], and [7], have taken up the study of ideals. This paper takes up the study of homomorphisms of (left) near-rings not subject to the condition 0.a = 0. It is shown that such homomorphisms can be decomposed into homomorphisms of two special sub-near-rings. Conversely, conditions are sought under which homomorphisms of the two sub-near-rings may be mated to produce a homomorphism of the sub-near-ring.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 35 - 41
Copyright
Copyright © Canadian Mathematical Society 1968

References

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