On Congruences Induced by Certain Relations on “Semigroups”

K. V. R. Srinivas

Department of Mathematics, Regency Institute of Technology, Yanam, India.

DOI: 10.4236/apm.2015.59054                

Abstract

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 to be the smallest semilattice congruence η is obtained.

Keywords

Cancellative “Semigroup”, Quasi-Separative ‘‘Semigroup’s”, Weakly Cancellative ‘‘Semigroup’s”, Weakly Balanced “Semigroup”

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Burmistrovich, I.E. (1965) Commutative Bands of Cancellative “Semigroup’s’”. Sib.Mat.Zh., 6, 284-299 (Russian).
[2]	Petritch, M. (1973) Introduction to “‘Semigroup’ Theory”. Merill Books, Columbus.
[3]	Krasilnikova, Yu.I. and Novikov, B.V. (2005) On Quasi-separative “semigroup’s”. “Semigroup” Forum, 70, 347-355.