Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...

We consider the identities of a variety of semigroup-related algebras modeling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interpret...

This article studies commutative orders, that is, commutative semigroups having a semigroup of quotients. In a commutative order S, the square-cancellable elements S(S) constitute a well-behaved separable subsemigroup. Indeed, S(S) is also an order and has a maximum semigroup of quotients R, which is Clifford. We present a new characterisation of commutative orders in terms of semilattice decom...

Work of Clifford, Munn and Ponizovskĭı parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Rees’s theorem characterizing 0-simple...

An algebraic structure is finitely related (has finite degree) if its term functions are determined by some finite set of finitary relations. We show that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Further we provide the first example of a semigroup that is not fi...

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalize...

A common generalization of the author's embedding theorem concerning the £-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an ortho...

The purpose of this paper is to characterize an ordered semigroup S in terms the properties associated B(S) all bi-ideals S. We show that a Clifford if and only semilattice. normal band both regular intra regular. For each subvariety V bands, we such ∈ V.

1. A. H. Clifford, Naturally totally ordered commutative semigroups, Amer. J. Math. 76(1954), 631-646. 2. , Totally ordered commutative semigroups, Bull. Amer. Math. Soc. 64 (1958), 305-316. 3. O. Holder, Die Axiome der Quantitât und die Lehre vom Mass, Ber. Verh. Sachs. Ges. Wiss. Leipzig Math.-Phys. Kl. 53 (1901), 1-64. 4. T. Tamura, Commutative nonpotent archimedean semigroup with cancellati...