Given a discrete and countable inverse semigroup $S$ one can study, in analogy to the group case, its geometric aspects. In particular, we equip with natural metric, given by path metric disjoint union of Sch\"{u}tzenberger graphs. This graph, which denote $\Lambda_S$, inherits much structure $S$. this article compare C*-algebra $\mathcal{R}_S$, generated left regular representation on $\ell^2(...

In this paper, we prove that the algebra of an étale groupoid with totally disconnected unit space has a simple over field if and only is minimal effective function vanishes on every open subset null function. Previous work subject required to be also topologically principal in non-Hausdorff case, but do not. Furthermore, provide first examples not groupoids spaces. Our come from self-similar g...

The idempotent problem of a finitely generated inverse semi-group is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent problem is necessarily finite. This answers a question of Gilbert and Noonan Heale, and establishes a gen-eralisation to inverse semigroups of Anisimov's Th...

The purpose of this paper is to investigate the dynamical systems in the context of topological semigroup actions in intuitionistic fuzzy 2-metric spaces. AMS Subject Classification : 46 S 40.

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Abstract We prove implications among the conditions in title for general $\text C^*$-inclusions $A\subseteq B$, and we also relate this to several other properties case $B$ is a crossed product an action of group, inverse semigroup, or étale groupoid on $A$. show that if C^*$-inclusion aperiodic it has unique pseudo-expectations, if, addition, pseudo-expectation faithful, then $A$ supports sens...

A factorizable inverse monoid can be identified, up to isomorphism, with an inverse submonoid M of a symmetric inverse monoid I(X) where each element of M is a restriction of a permutation of X belonging to M . So factorizable inverse monoids are natural objects, and appear in a number of branches of mathematics, cf. [12], [4]. The notion of an almost factorizable inverse semigroup was introduc...

In this paper we prove two new results about closed semigroups in the family of solvable groups Hmn := R nφ R where φ, the structure homomorphism, maps nontrivially into the center of Aut(Rn). The rst result states that the closure of a semigroup generated by a set in Hmn that is not included in a maximal semigroup with nonempty interior is actually a group. The second result states that among ...