Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups - Billhardt, B. (2013)
An associate inverse subsemigroup of a regular semigroup S is a subsemi- group T of S containing a least associate x* of each x in S, in relation to the natural partial order <. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all *-homomorphisms and all *-congruences on such semigroups.