A SPECIAL CASE OF NEAR â€“ 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