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A Characterization of semiprime ideals in near-rings

Part of: Algebraic structures

Published online by Cambridge University Press:  09 April 2009

V. Sambasiva Rao
V. Sambasiva Rao
Affiliation:
Department of Mathematics, Nagarjuna University, Nagarjunanagar-522 510, A. P., India
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Abstract

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It is well known that in any near-ring, any intersection of prime ideals is a semiprime ideal. The aim of this paper is to prove that any semiprime ideal I in a near-ring N is the intersection of all minimal prime ideals of I in N. As a consequence of this we have any seimprime ideal I is the intersectionof all prime ideals containing I.

MSC classification

Secondary: 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 212 - 214
Copyright
Copyright © Australian Mathematical Society 1982

References

Pilz, G. (1977), Near-rings (North-Holland, Amsterdam-New York).Google Scholar