A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M[G; I,Λ;P ] , is given. The result generalises that of Ruškuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of |I| , |Λ| , the number of connected components k of P and a number rmin which we define. We go on to show that t...

the main purpose of this paper is to establish a relation between universality of certain p-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. in particular, we show that if we take p to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, the...

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

By a 'representation' we shall mean throughout a representation by n x n matrices with entries from an arbitrary (commutative) field. Clifford has constructed all representations of completely simple semigroups [1; 4]. Munn has determined the representations of finite semigroups for which the corresponding semigroup algebra is semi-simple [6]. It is noted by Clifford and Preston [4] that if S i...

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals bi-ideals. We also characterize the left right simple completely semigroups utilizing show that S is if only it simple. prove then each ideal ˜jµ S, have ˜jµ(r1r2) = ˜jµ(r2r1) all r1, r2 ∈ S.

Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a squar...