Denumerants of numerical semigroups are known to be difficult to obtain, even with small embedding dimension of the semigroups. In this work we give some results on denumerants of 3-semigroups S = 〈a, b, c〉. The time efficiency of the resulting algorithms range from O(1) to O(c). Closed expressions are obtained under certain conditions.

This paper determines all pseudovarieties of nite semigroups whose powers are contained in DA. As an application, it is shown that it is computable, for a decidable pseudovariety V of aperiodic semigroups, the least exponent n such that the iterated power P n V is the pseudovariety of all nite semigroups.

For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open to...

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...

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discus...

In any semigroup S, we say that elements a and b are left inverses of each other if a = aba, b = bab and a L b, in which case we write a γ b. Right inverses are defined dually with the notation δ. Set τ = δγ. We study the classes of semigroups in which τ has some of the usual properties of a relation. We also consider properties of (maximal) completely simple subsemigroups of S. In terms of the...

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper we present a new definition of conjugacy, which can be applied to an arbitrary semigroup, including semigroups with zero. We characterize this conjugacy in various semigro...

We study positive C0-semigroups on Lp associated with second order uniformly elliptic divergence type operators with singular lower order terms, subject to a wide class of boundary conditions. We obtain an interval (pmin, pmax) in the Lp-scale where these semigroups can be defined, including the case 2 6∈ (pmin, pmax). We present an example showing that the result is optimal. We also show that ...

In a recent paper, P.G. Trotter and the author introduced a \regular" semidirect product UV of e-varieties U and V. Among several speciic situations investigated there was the case V = RZ, the e-variety of right zero semigroups. Applying a covering theorem of McAlister, it was shown there that in several important cases (for instance for the e-variety of inverse semigroups), U RZ is precisely t...

In studying a general semigroup S, a natural thing to do is to decompose 5 (if possible) into the class sum of a set {Sa; aCl} of mutually disjoint subsemigroups Sa such that (1) each Sa belongs to some more or less restrictive type 13 of semigroup, and (2) the product SaSfi of any two of them is wholly contained in a third: SaSpClSy, for some yCI depending upon a and /3. We shall then say that...