J Austral Math Soc Ser A 43 pp64--69, 1987.

Congruences and Green's Relations on Eventually Regular Semigroups

P. M. Edwards

Abstract

A semigroup is eventually regular if each of its elements has some power that is regular. Let K be one of Green's relations and let r be a congruence on an eventually regular semigroup S. It is shown for K = L, R and D that if A and B are regular elements of S/r that are K-related is S/r then there exist elements a Î A, b Î B such that a and b are K-related in S. The result is not true for H or J.

1980 AMS Subject Classification: 20M10

Browse the article

Authors

P. M. Edwards

Department of Econometrics, Monash University, Clayton, Victoria 3168, Australia.