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On Near-Rings of Quotients

Published online by Cambridge University Press:  20 January 2009

A. Oswald
A. Oswald
Affiliation:
Department of Mathematics, Teesside Polytechnic, Middlesbrough, Cleveland, England
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In (2), Holcombe investigated near-rings of zero-preserving mappings of a group Γ which commute with the elements of a semigroup S of endomorphisms of Γ and examined the question: under what conditions do near-rings of this type have near-rings of right quotients which are 2-primitive with minimum condition on right ideals? In the first part of this paper (§2) we investigate further properties of near-rings of this type. The second part of the paper (§3) deals with those near-rings which have semisimple near-rings of right quotients. Our results here are analogous to those of Goldie (1); in particular, with a suitable definition of finite rank we prove that a near-ring which has a semisimple near-ring of right quotients has finite rank

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 77 - 86
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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