%0 Journal Article
%T Idempotent separating congruence on a regular semigroup with a regular idempotent
%A K. Indhira
%A V. M. Chandrasekaran
%J Advanced Studies in Theoretical Physics
%D 2013
%I 
%X Let S be a regular semigroup. A congruence ¦Ñ on S is called idempotentseparating if the associated projection homomorphism ¦Ñ # : S ¡ú S| ¦Ñ , isidempotent separating. Hall shows that if u is an idempotent of a regularsemigroup S then every idempotent-separating congruence on uSu extends to aunique idempotent separating congruence on SuS. An idempotent u of a regularsemigroup S is called regular if fuR fL uf for each f ¡Ê E(S). In this paper, weproved that if u is a regular idempotent of S then S = SuS. Also we find therelationship between the idempotent separating congruence on S and uSu, when uis a regular idempotent of S.
%K regular semigroup
%K coextension
%K idempotent separating congruence
%K regular idempotent
%U http://www.m-hikari.com/astp/astp2013/astp1-4-2013/chandrasekaranASTP1-4-2013.pdf