Congruences and Green’s relations on eventually regular semigroups. (English) Zbl 0624.20041

A semigroup is called eventually regular if each of its elements has some power that is regular. In this paper it is proven that Green’s relations \({\mathcal L}\), \({\mathcal R}\), \({\mathcal D}\) can be lifted along any homomorphism between eventually regular semigroups. For \({\mathcal H}\) and \({\mathcal J}\) this property fails even for regular semigroups. The proof follows the one used by T. E. Hall [Glasg. Math. J. 13, 167-175 (1972; Zbl 0257.20057)] in the regular case.
Reviewer: L.Márki


20M10 General structure theory for semigroups
20M15 Mappings of semigroups


Zbl 0257.20057