Ultragraphs give rise to labelled graphs. We realize algebras associated such graphs as groupoid algebras, generalizing a known algebra realization of ultragraph C*-algebras any ultragraph. Then, we characterize the shift space an tight spectrum inverse semigroup with via its graph. In purely algebraic setting, show that partial action used describe Leavitt path skew group ring is equivalent du...

In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid End(A) of a countable relational structure A. As applications, show that monoids several well-known structures, including random graph, directed partial order, possess unique Polish topology. every case topology is subspace induced by usual Baire space NN. We also m...

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

We study topological aspects of the category abstract Cuntz semigroups, termed Cu. provide a suitable setting in which we are able to uniformly control how approach an element Cu-semigroup by rapidly increasing sequence. This approximation induces semimetric on set Cu-morphisms, generalizing Cu-metrics that had been constructed past for some particular cases. Further, develop approximate intert...

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T. Tamura for N-semigroups.

We derive the actions for type II Green-Schwarz strings up to second order in the fermions, for general bosonic backgrounds. We base our work on the so-called normal coordinate expansion. The resulting actions are κ-symmetric and, for the case of surviving background supersymmetries, supersymmetric. We first obtain the type IIa superstring action from the 11D supermembrane by double dimensional...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free...

Inspired by the results of [APR], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebr...

Let A∗ denote the free monoid generated by a finite nonempty set A. In this paper we introduce a new measure of complexity of languages L ⊆ A∗ defined in terms of the semigroup structure on A∗. For each L ⊆ A∗, we define its cost c(L) as the infimum of all real numbers α for which there exist a language S ⊆ A∗ with pS(n) = O(n) and a positive integer k with L ⊆ S.We also define the cost dimensi...