, Volume 87, Issue 1, pp 120-128,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 18 Aug 2012

Rectangular group congruences on a semigroup


We study rectangular group congruences on an arbitrary semigroup. Some of our results are an extension of the results obtained by Masat (Proc. Am. Math. Soc. 50:107–114, 1975). We show that each rectangular group congruence on a semigroup S is the intersection of a group congruence and a matrix congruence and vice versa, and this expression is unique, when S is E-inversive. Finally, we prove that every rectangular group congruence on an E-inversive semigroup is uniquely determined by its kernel and trace.

Communicated by Marcel Jackson.