E-INVERSIVE *-SEMIGROUPS
Shoufeng Wang, Yinghui Li · Communications of the Korean Mathematical Society · 2012
(S, *) is a semigroup S equipped with a unary operation "*". This work is devoted to a class of unary semigroups, namely E- $inversive$ *- $semigroups$ . A unary semigroup (S, *) is called an E-inversive *-semigroup if the following identities hold: $$x^*xx^*=x^*$$ , $$(x^*)^*=xx^*x$$ , $$(xy)^*=y^*x^*$$ . In this paper, E-inversive *-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.