A SPECIAL CASE OF NEAR – IDEMPOTENT SEMIGROUPS - Kavitha, T.N. (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 relationsÂ Î», Ï andÂ Î´.Â In this paper, we introduce a new pair of relationsÂ Â Î»rÂ Â andÂ Â Ïr Â Â on a near idempotent semigroup.Â In generalÂ Â Î»rÂ Â andÂ Â ÏrÂ Â are not reflexive relations on a near idempotent semigroup and hence not equivalence relations. We study the special case whenÂ Î»rÂ becomes reflexive on a near idempotent semigroup.Â 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