%0 Journal Article
%T On Congruences Induced by Certain Relations on ¡°Semigroups¡±
%A K. V. R. Srinivas
%J Advances in Pure Mathematics
%P 579-582
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.59054
%X In his paper ¡°On quasi-separative ¡®semigroup¡¯s¡¯¡±, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a ¡°semigroup¡±. They further showed that if the ¡°semigroup¡± is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ¡®¡®semigroup¡¯s¡±. In this paper mainly it is observed that if S is a quasi-separative and regular ¡°semigroup¡± then the necessary and sufficient condition for <img alt=\"\" src=\"Edit_9e308171-c91a-4a48-9fe6-2f8b6ac90c74.jpg\" />to be the smallest semilattice congruence ¦Ç is obtained.
%K Cancellative ¡°Semigroup¡±
%K Quasi-Separative ¡®¡®Semigroup¡¯s¡±
%K Weakly Cancellative ¡®¡®Semigroup¡¯s¡±
%K Weakly Balanced ¡°Semigroup¡±
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=58498