A SPECIAL CASE OF NEAR – IDEMPOTENT SEMIGROUPS

In a previous paper we introduced a near idempotent semigroup and studied its structure through the relations  λ, ρ and  δ.  In this paper, we introduce a new pair of relations   λ r and   ρ r   on a near idempotent semigroup.  In general   λ r   and   ρ 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