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...

In this paper, we introduce a new class algebras related to BCK-algebras and semigroups, called a KS-semigroup and define an ideal of a KS-semigroups and a strong KS-semigroup, and characterizations of ideals is given. Also we define a congruence relation on a KS-semigroups and a quotient KS-semigroups and prove the isomorphism. Mathematics Subject Classification: 06F35, 03G25

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,

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer seq...

The main aim of this paper is to study fuzzy congruences of typeB semigroups. After obtaining some properties and characterizations of fuzzy good congruences on adequate semigroups, we consider fuzzy good congruences on type-B semigroups. Finally, we prove a theorem giving equivalent conditions on fuzzy cancellative congruences of such semigroups. Mathematics Subject Classification: 06F05; 20M10

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

The classification of finite semigroups is difficult even for small orders because of their large number. Most finite semigroups are nilpotent of nilpotency rank 3. Formulae for their number up to isomorphism, and up to isomorphism and anti-isomorphism of any order are the main results in the theoretical part of this thesis. Further studies concern the classification of nilpotent semigroups by ...

The genus of a numerical semigroup is the size of its complement. In this paper we will prove some results about counting numerical semigroups by genus. In 2008, Bras-Amorós conjectured that the ratio between the number of semigroups of genus g + 1 and the number of semigroups of genus g approaches φ, the golden ratio, as g gets large. Though several recent papers have provided bounds for count...

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups " expanding automaton semigroups ". W...