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1982•Journal of the Australian Mathematical Society Series A Pure Mathematics and StatisticsOpen access

A Characterization of semiprime ideals in near-rings

V. S. Rao

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Abstract

Abstract 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.

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Abstract 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.

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Available abstract

Abstract 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.

Key concepts: Semiprime ring, Mathematics, Semiprime, Intersection (aeronautics), Ideal (ethics), Associated prime, Prime (order theory), Minimal ideal

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