A SPECIAL CASE OF NEAR – IDEMPOTENT SEMIGROUPS

Abstract

In a previous paper we introduced a near idempotent semigroup and studied its structure through the relations  λ, Ï and  δ.  In this paper, we introduce a new pair of relations   λ_r   and   Ï_r   on a near idempotent semigroup.  In general   λ_r   and   Ï_r   are not reflexive relations on a near idempotent semigroup and hence not equivalence relations. We study the special case when  λ_r  becomes reflexive on a near idempotent semigroup.  This gives rise to a special case of a near idempotent semigroup, namely, a right near idempotent semigroup.

Key words: Near idempotent semigroup, right near idempotent semigroup, reflexive relations, and equivalence relations