the aim of this paper is to study semigroups possessing $e$-regular elements, where an element $a$ of a semigroup $s$ is {em $e$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ esubseteq e(s)$. where $s$ possesses `enough' (in a precisely defined way) $e$-regular elements, analogues of green's lemmas and even of green's theorem hold, where green&apos...

In this paper we study sub-semigroups of a zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor graphs. We study properties of sub-semigroups of Boolean semigroups via the zero-divisor graph. As an application, we provide a characterization of the graphs which ar...

This paper is a survey of recent results in the theory of nite semigroups using syntactic techniques. This involves manipulating pseudoidentities and the study of relatively free proonite semigroups, whose structure encodes algebraic and combinatorial properties common to the members of a pseudovariety of semigroups. These techniques are illustrated with applications in the study of semigroups ...

Abstract. We introduce a class of time-inhomogeneous transition operators of Feynman-Kac type that can be considered as a generalization of symmetric Markov semigroups to the case of a time-dependent reference measure. Applying weighted Poincaré and logarithmic Sobolev inequalities, we derive L → L and L → L estimates for the transition operators. Since the operators are not Markovian, the esti...

Even though the study and relevance of maximal embedding dimension numerical semigroups arises in a natural way among the other numerical semigroups, they have become specially renowned due to the existing applications to commutative algebra via their associated semigroup ring (see for instance [1, 5, 15, 16, 99, 100]). They are a source of examples of commutative rings with some maximal proper...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

We generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using Rota’s theory of Möbius inversion. The technique works for a large class of semigroups including: inverse semigroups, semigroups with commuting idempotents, idempotent semigroups and semigroups with basic algebras. Using these tools we are able to give a complete descr...

The five-element Brandt semigroup B2 and its four-element subsemigroup B0, obtained by omitting one nonidempotent, have played key roles in the study of varieties of semigroups. Regarded in that fashion, they have long been known to be finitely based. The semigroup B2 carries the natural structure of an inverse semigroup. Regarded as such, in the signature {·,−1 }, it is also finitely based. It...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

A class of [r]-semigroups, extending the class of smooth distribution semigroups of Balabane and Emami-Rad, is introduced. Relations with integrated semigroups of Arendt are given as well as a generalization of deLaubenfels and Jazar’s result on relations between smooth semispectral distributions and integrated semigroups. AMS Mathematics Subject Classification (2000): 47D60,