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2008•Kyungpook mathematical journalRequires access

On the Ideal Extensions in Γ-Semigroups

Manoj Siripitukdet, Aiyared Iampan

Open publisher page 7 citations

Abstract

In 1981, Sen [4] have introduced the concept of -semigroups. We have known that -semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in -semigroups and characterize the relationship between the extensions of ideals and some congruences in -semigroups.

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What this paper is about

In 1981, Sen [4] have introduced the concept of -semigroups. We have known that -semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in -semigroups and characterize the relationship between the extensions of ideals and some congruences in -semigroups.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In 1981, Sen [4] have introduced the concept of -semigroups. We have known that -semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in -semigroups and characterize the relationship between the extensions of ideals and some congruences in -semigroups.

Key concepts: Semiprime ring, Mathematics, Semiprime, Congruence relation, Prime (order theory), Generalization, Boolean prime ideal theorem, Pure mathematics

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