A semigroup is called eventually regular if each of its elements has a regular power. In this paper we study certain fundamental congruences on an eventually regular semigroup. We generalize some results of Howie and Lallement (1966) and LaTorre (1983). In particular, we give a full description of the semilattice of group congruences (together with the least such a congruence) on an arbitrary eventually regular (orthodox) semigroup. Moreover, we investigate UBG-congruences on an eventually regular semigroup. Finally, we study the eventually regular subdirect products of an E-unitary semigroup and a Clifford semigroup.
Ćiric, M. and Bogdanowić, S., Sturdy bands of semigroups, Collect. Math., 41 (1980), 189–195.
Ćiric, M. and Bogdanowić, S., Sturdy bands of semigroups, Collect. Math., 41 (1980), 189–195.)| false