A SPECIAL CASE OF NEAR – IDEMPOTENT SEMIGROUPS
T. Kavitha · Journal of Global Research in Mathematical Archives(JGRMA) · 2018
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