Semigroup Forum

, Volume 87, Issue 1, pp 120-128

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Rectangular group congruences on a semigroup

  • Roman S. GigońAffiliated withInstitute of Mathematics and Computer Science, Wroclaw University of Technology Email author 


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.


Rectangular group congruence Group congruence Matrix congruence