Associate subgroups of orthodox semigroups

Beyond Orthodox Semigroups

We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of semigroups which we name weakly B-orthodox. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. Here B denotes a band of idempotents; we note that if B is a semilattice then a weakly B-or...

Unary Semigroups with an Associate Subgroup

Regular Semigroups with a S 0 − Orthodox Transversal

In this paper, we consider another generalization for quasi-ideal orthodox transversal, the so-called S0-orthodox transversals. We give a structure theorem for regular semigroups with S0-orthodox transversals. If S0 is a S0-orthodox transversal of S then S can be described in terms of S0. Mathematics Subject Classification: 20M10

Homomorphisms and Congruences of Medial Semigroups with an Associate Subgroup

Let S be the model of a semigroup with an associate subgroup whose identity is a medial idempotent constructed by Blyth and Martins considered as a unary semigroup. For another such semigroup T , we construct all unary homomorphisms of S into T in terms of their parameters. On S we construct all unary congruences again directly from its parameters. This construction leads to a characterization ...

Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x∗ of each x ∈ S, in relation to the natural partial order ≤S in S. 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 ∗-congruences on such class of semigroups.