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1992•Bulletin of the Australian Mathematical SocietyOpen access

Lattice of idempotent separating congruences in a ℙ-regular semigroup

M. K. Sen, A. Seth

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Abstract

In this paper we introduce the concept of ℙ-regular, normal subset of a ℙ-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a ℙ-regular semigroup and finally describe the lattice of the idempotent separating congruences in a ℙ-regular semigroup.

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What this paper is about

In this paper we introduce the concept of ℙ-regular, normal subset of a ℙ-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a ℙ-regular semigroup and finally describe the lattice of the idempotent separating congruences in a ℙ-regular semigroup.

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Available abstract

In this paper we introduce the concept of ℙ-regular, normal subset of a ℙ-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a ℙ-regular semigroup and finally describe the lattice of the idempotent separating congruences in a ℙ-regular semigroup.

Key concepts: Mathematics, Congruence relation, Idempotence, Semigroup, Regular semigroup, Bicyclic semigroup, Congruence (geometry), Lattice (music)

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