Let A be a simple, separable C∗-algebra of stable rank one. We prove that the Cuntz semigroup of C(T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yield...

In this paper we will be on erned with the possibility of embedding a nite semigroup S into a nite 2-generated semigroup T that shares properties with S. In parti ular we show that any nite orthodox semigroup S may be embedded in a nite orthodox semigroup T generated by two group elements and that any nite orthodox monoid S1 may be embedded as a semigroup into a nite 2-generated orthodox monoid...

It is now well known that curvature conditions à la Bakry-Émery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein distance. However, this curvature condition may include a dimensional correction which up to now had not induced any strenghtening of this contraction. We first consider the simplest example of the Euclidean heat semig...

The author proves that, if S is an FIC-semigroup or a completely regular semigroup, and if RS is a ring with identity, then R < E(S) > is a ring with identity. Throughout this paper, R denotes as a ring with identity. Let S be a semigroup, X ⊆ S . The following notations are used in the paper: < X > : the subsemigroup of S generated by X ; |X| : the cardinal number of X ; E(S): the set of idemp...

Garcia and Stichtenoth discovered two towers of function fields that meet the Drinfeld-Vlăduţ bound on the ratio of the number of points to the genus. For one of these towers, Garcia, Pellikaan and Torres derived a recursive description of theWeierstrass semigroups associated to a tower of points on the associated curves. In this article, a non-recursive description of the semigroups is given a...

(sg2) T(0)x = x for all x ∈ C; (sg3) T(s+ t) = T(s)◦T(t) for all s, t ≥ 0; (sg4) for each x ∈ C, the mapping t → T(t)x is continuous. We know that {T(t) : t ≥ 0} has a common fixed point under the assumption that C is weakly compact convex and E has the Opial property; see [3, 4, 5, 6, 8, 10, 12] and other works. Convergence theorems for one-parameter nonexpansive semigroups are proved in [1, 2...

Quasi-ideals were introduced by Otto Steinfeld [43] as those non-empty subsets Q of a semigroup T satisfying QTD TQ c Q. When T is regular they are precisely the subsets Q of T which satisfy QTQ = Q ([43, Theorem 9.3]). There are many examples of quasi-ideals in regular semigroup theory. We list below some of the most important: • Every subsemigroup of the form eSe (where e is an idempotent) is...

Several algebraic structures have been studied by many authors to discuss the relationships among them. This article aims study two structures, namely semigroup and BA-algebra, combining them in one form, BA-semigroup investigate some of its properties. paper BA-sub-semigroup, an ideal BA-homomorphism a with their Some examples are given illustrate results.

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...

We consider the set of equational classes of finite functions endowed with the operation of class composition. Thus defined, this set gains a semigroup structure. This paper is a contribution to the understanding of this semigroup. We present several interesting properties of this semigroup. In particular, we show that it constitutes a topological semigroup that is profinite and we provide a de...