We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it. Background and motivation The main results of this paper were motivated by one of the fundamental theorems of Imre Simon, namely, by his elegant algebraic characterization of the class of piecewise testable languages [21, 22]. Th...

The main purpose of this paper is to establish a relation between universality of certain P-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. In particular, we show that if we take P to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, t...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12

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...

This paper studies automatic structures for subsemigroups of Baumslag–Solitar semigroups (that is, semigroups presented by ⟨x, y | (yx, xy)⟩ where m,n ∈ N). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m > n, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If m < n, all of its finitely generated subsemigroups ...

the main purpose of this paper is to establish a relation between universality of certain p-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. in particular, we show that if we take p to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, the...

A Schmidt group is a non-nilpotent finite group in which each proper subgroup is nilpotent. Each Schmidt group G can be described by three parameters p, q and v, where p and q are different primes and v is a natural number, v ≥ 1. Denote by S the class of all Schmidt groups which have the same parameters p, q and v. It is shown in this paper that the class S can be characterized by the properti...