In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

In a previous paper, the author has introduced a number of homomorphisms of an arbitrary semigroup into the translational hull of certain Rees matrix semigroups or orthogonal sums thereof. For regular semigroups, it is proved here that all of these homomorphisms have the property that the image is a densely embedded subsemigroup, i.e., is a densely embedded ideal of its idealizer, and that the ...

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same range.

For some distinguished properties of semigroups, such as having idempotents, regularity, hopficity etc, we study the following: whether that property or its negation is a Markov property, whether it is decidable for finitely presented semigroups and for one-relation semigroups and monoids. All the results and open problems are summarized in a table.

We construct a modification of Churchill and Trotter’s trifree objects in e-varieties of locally E-solid semigroups, which have the property, for e-varieties of locally inverse semigroups and for e-varieties of Esolid semigroups, of being isomorphic to the bifree objects.

Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann’s theorem answering a question of Paul Erdös. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to a...

In this note, we show that an ordered ternary semigroup is left and right simple if and only if it does not contain proper bi-ideals. The similar result is valid on ordered semigroups [7], on ordered Γ-semigroups [3] and on ternary semigroups [4]. Mathematics Subject Classification: 06F05

We present some new results on the existence and the approximationof common fixed point of expansive mappings and semigroups in probabilisticmetric spaces.

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

This is a survey of the theory of enveloping semigroups in topological dynamics. We review the, already classical, theory of enveloping semigroups, due mainly to Robert Ellis, and then proceed to describe some new connections which were discovered in the last few years between three seemingly unrelated theories: of enveloping semigroups, of chaotic behavior, and of representation of dynamical s...