It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proved to be decidable.

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.

It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-pr...

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

In this paper, we apply the theory of inverse semigroups to the C∗-algebra U [Z] considered in [Cun08]. We show that the C∗-algebra U [Z] is generated by an inverse semigroup of partial isometries. We explicity identify the groupoid Gtight associated to the inverse semigroup and show that Gtight is exactly the same groupoid obtained in [CL10].

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 ...

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.