**InternationaleJournals**

**Congruence
on Bi-Simple inverse ****w****-Semigroup of Left Quotient**

Department of Mathematics and Statistics, University of Port Harcourt, Rivers State, Nigeria. Email: ueiboei@yahoo.com

**ABSTRACT**

We construct the congruence r on Bisimple inverse w-semigroup Q of left quotients S and show that congruence on S can be carried to its order Q. We also show that there is group congruence on Q and H is a congruence on Q, indeed its maximum congruence. This helps us to deduce some nice properties of this congruence on Q.

**AMS Classification No: 20H18**

**Key Words: Bi-Simple
Semigroup, Congruence, Left Orders, Green’s Relations.**

**International
eJournal of Mathematical Sciences, Technology and Humanities**

**Volume** **3**,
**Issue** **2**, **Pages**: ** **1045 - 1055