A topological semigroup is a nonvoid, Hausdorff space, 5, together with a continuous, associative multiplication defined on 5. Here the term semigroup will always denote a topological semigroup. In [4], Wallace and Koch have shown that if the circle, B, is a semigroup such that B2 = B, then either B is a group, or the multiplication on B is of the trivial kind xy = x, or xy = y. In [6], Mostert...

We study algebraic and topological properties of the convolution semigroups of probability measures on topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P (G) over some topological group G if and only if S embeds into the semigroup exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maxi...

Let S be a semigroup. In certain cases we give some characterizations of extreme amenability of S and we show that in these cases extreme left amenability and extreme right amenability of S are equivalent. Also when S is a compact topological semigroup, we characterize extremely left amenable subalgebras of C(S), where C(S) is the space of all continuous bounded real valued functions on S

In this paper, we introduce a generalized class of an Hv-semigroup obtained from an LA-semigroup H. This generalized Hv-structure is called an Hv-LA-semigroup. We provide several examples of Hv-LA-semigroups. Moreover, with the help of an example we obtain that each LA-semigroup endowed with an equivalence relation can induce an Hv-LA-semigroup. We also investigate isomorphism theorems with the...

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...