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2001•Scientiae mathematicae JaponicaeRequires access

ON PRIME AND SEMIPRIME IDEALS IN GAMMA-SEMINEAR-RINGS

Kim Kyung Ho

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Abstract

In this paper, we introduce the notion of prime and semiprime ideal and characterize prime and semiprime ideals in a -seminear-ring. Among them, for any -seminear-ring, an ideal is semiprime if and only if it is the intersection of all primes containg it. Moreover, an ideal of a -seminear-ring is prime if and only if it is semiprime and strongly irreducible.

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What this paper is about

In this paper, we introduce the notion of prime and semiprime ideal and characterize prime and semiprime ideals in a -seminear-ring. Among them, for any -seminear-ring, an ideal is semiprime if and only if it is the intersection of all primes containg it. Moreover, an ideal of a -seminear-ring is prime if and only if it is semiprime and strongly irreducible.

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Available abstract

In this paper, we introduce the notion of prime and semiprime ideal and characterize prime and semiprime ideals in a -seminear-ring. Among them, for any -seminear-ring, an ideal is semiprime if and only if it is the intersection of all primes containg it. Moreover, an ideal of a -seminear-ring is prime if and only if it is semiprime and strongly irreducible.

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

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