Narrow Results

It was first proved by McAlister in 1983 that every locally inverse semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup and Lawson in 2000 further generalized this result to some special locally adequate semigroups. In this paper, we show how these results can be extended to a class of locally Ehresmann semigroups.

Let X be a set with |X| ≥ 3, the full transformation semigroup on X, and E an equivalence relation on X. Let T_E(X) be the set of transformations f in which preserve E, i.e., (x,y) ∈ E implies (f(x),f(y)) ∈ E. It is known that T_E(X) is a subsemigroup of . In this paper, we describe the equivalence relations E so that the semigroup T_E(X) is abundant.

In this survey article, we will briefly introduce the recent development of rpp semigroups, its generalizations and some of its special subclasses. Some methods of constructions for such semigroups are introduced. Several structure theorems of such semigroups are described.