This paper concerns a number of diagram categories, namely the partition, planar Brauer, partial Motzkin and Temperley–Lieb categories. If [Formula: see text] denotes any these if is fixed morphism, then an associative operation may be defined on by text]. The resulting semigroup called sandwich semigroup. We conduct thorough investigation semigroups, with emphasis structural combinatorial prop...

In that paper, we prove an equivalence between Nash-type inequalities and an exponential decay (in the sense of the definition 2.2) for symmetric submarkovian semigroups. This exponential decay generalizes the notion of spectral gap where this number is replaced by a function. We discuss different formulations of the decay associated to the usual Nash inequality in terms of Lyapunov-type functi...

Let Λ be some class of Abelian groups. We say that a group A ∈ is determined by its endomorphism semigroup E⋆(A) in if the isomorphism ≅ E⋆(B), where B Λ, implies B. describe split groups $$ {\mathcal{QD}}_{\mathrm{cd}} completely decomposable quotient divisible their semigroups .

In this paper we compute the minimal degree of a faithful representation by partial transformations finite semigroup admitting completely reducible matrix over field complex numbers. This includes all inverse semigroups, and hence our results generalize earlier Easdown Schein on an semigroup. It also well-studied monoids like full fields monoid binary relations (i.e., matrices Boolean semiring)...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. The purpose of this paper is to introduce a generalization of ideas presented in [20]. Indeed, we study the concept of intuitionistic fuzzy interior ideals of a Γ-semigroup, by using Atanassov’s idea and investigate some of their important properties. Specially, we obtain a chara...

The (.)reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show that (S)reg can be described by a rather simple complete string rewrite system, as a consequence of which we obtain a new proof of the normal form theorem for (S)...

A characterization of perfect semigroup rings A[G] is given by means of the properties of the ring A and the semigroup G. It was proved in [10] that for a ring with unity A and a group G the group ring A[G] is perfect if and only if A is perfect and G is finite. Some results on perfectness of semigroup rings were obtained by Domanov [3]. He reduced the problem of describing perfect semigroup ri...