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 ...

By using the theory of semigroups, we prove the compactness of the difference between the semigroups generated by the system of thermoviscoelasticity type and its decoupled system, respectively.

The endomorphism semigroup for a class of commutative semigroups, called special semigroups, will be studied their structures will be determined in some important cases. AMS Classification : 20

This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under...

We show that for a discrete semigroup S there exists a uniquely determined complete Boolean algebra B(S) the algebra of clopen subsets of M(S). M(S) is the phase space of the universal minimal dynamical system for S and it is an extremally disconnected compact Hausdorff space. We deal with this connection of semigroups and complete Boolean algebras focusing on structural properties of these alg...

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizati...

We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of semigroups which we name weakly B-orthodox. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. Here B denotes a band of idempotents; we note that if B is a semilattice then a weakly B-or...

We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4, 6 + 4k, 87− 4k) and S(9, 3 + 9k, 85− 9k) generated by three elements. We present a generalization of these sequences by numerical semigroups S(r 1 , r1r2 + r 2 1k, r3 − r 2 1k), k ∈ Z, r1, r2, r3 ∈ Z , r1 ≥ 2 and gcd(r1, r2) = gcd(r1, r3) = 1, and calculate their univers...

The Brauer semigroup Bn of partitions of a 2n-element set into two-element subsets, can be generalized in various ways. For example we may consider arbitrary partitions to obtain the semigroup Cn. The visualization of elements of these semigroups as chips leads us to the Temperley-Lieb semigroup TLn and its analogue TLCn. We study combinatorial properties of these four semigroups. For example, ...

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960’s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green’s relation J is tri...