We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Using different descriptions of the Cuntz semigroup and Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated semigroup, a unique lower semicontinuous $2$-quasitrace whose stabilization has stable rank $1$ are either or algebraically simple.

We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0Hecke algebras.

Let G ⊆ ω be a semigroup. G polyadic algebras with equality, or simply G algebras, are reducts of polyadic algebras with equality obtained by restricting the similarity type and axiomatization of polyadic algebras to substitutions in G, and possibly weakening the axioms governing diagonal elements. Such algebras were introduced in the context of ’finitizing’ first order logic with equality. We ...

The universal abelian, band, and semilattice compactifications of a semitopological semigroup are characterized in terms of three function algebras. Some relationships among these function algebras and some well-known ones, from the universal compactification point of view, are also discussed.

We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations. AMS Subject Classification: 20M18; 16S99; 20M30; 05E10

let $s$ be an inverse semigroup and let $e$ be its subsemigroup of idempotents. in this paper we define the $n$-th module cohomology group of banach algebras and show that the first module cohomology group $hh^1_{ell^1(e)}(ell^1(s),ell^1(s)^{(n)})$ is zero, for every odd $ninmathbb{n}$. next, for a clifford semigroup $s$ we show that $hh^2_{ell^1(e)}(ell^1(s),ell^1(s)^{(n)})$ is a banach space,...