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2008•Communications of the Korean Mathematical SocietyRequires access

WEAKLY PRIME LEFT IDEALS IN NEAR-SUBTRACTION SEMIGROUPS

Patchirajulu Dheena, G. Kumar

Open publisher page 8 citations

Abstract

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$ -system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

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What this paper is about

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$ -system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$ -system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

Key concepts: Mathematics, Prime (order theory), Ideal (ethics), Minimal ideal, Prime ideal, Associated prime, Radical of an ideal, Semigroup

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