The elementary result of Variety theory is Eilenberg’s Variety theorem which was motivated by characterizations of several families of string languages by syntactic monoids or semigroups, such as Schützenberger’s theorem connecting star-free languages and aperiodic monoids. Eilenberg’s theorem has been extended in various directions. For example, Thérien involved varieties of congruences on fre...

This paper is concerned with the behavior of semigroups of nonlinear contractions on closed convex subsets of a Hilbert space H. Recently, many results, known for semigroups of linear operators, were extended to semigroups of nonlinear contractions. The first results in this direction by Neuberger [25] and oharu [26] dealt mainly with the representation of such semigroups by means of exponentia...

The Ehresmann-Schein-Nambooripad (ESN) Theorem, stating that the category of inverse semigroups and morphisms is isomorphic to the category of inductive groupoids and inductive functors, is a powerful tool in the study of inverse semigroups. Armstrong and Lawson have successively extended the ESN Theorem to the classes of ample, weakly ample and weakly E-ample semigroups. A semigroup in any of ...

In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...

Profinite semigroups may be described shortly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a classifying tool for rational languages. Of particular relevance are relatively free profinite semigroups which for pseudovarieties play the role of free algebras in the theory of varieties. Combinatorial pro...

The concept of σ-reflexive semigroups is due to Chacron and Thierrin in 1972. In the present paper we discuss σ-reflexive semigroups with apartness. We prove some fundamental properties of these semigroups.

Goes to the advanced topics rather fast. Contains up-to-date proofs for free inverse semigroups, topics on biordered sets, Isbell's zigzags , and some combinatorics of transformation semigroups.] Fundamentals of semigroup theory, 1995. [Probably the best introduction. Contains more advanced material such as Isbell's zigzags , and the free inverse semi-groups]. G. Lallement, Semigroups and combi...

We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...

In this paper, we discuss properties of medial idempotents on abundant semigroups, study quasi-adequate semigroups with a normal medial idempotent and some of their extreme cases, and give a description of structure of every type of such semigroups, respectively.

A class of regular semigroups closed under taking direct products, regular subsemigroups, and homomorphic images is an existence-variety (or evariety) of regular semigroups. Each e-variety of locally inverse semigroups can be characterized by a set of bi-identities. These are identities of terms of type (2, 2) in two sorts of variables X and X'. In this paper we obtain a basis of bi-identities ...