we present a characterization of arens regular semigroup algebras $ell^1(s)$, for a large class of semigroups. mainly, we show that if the set of idempotents of an inverse semigroup $s$ is finite, then $ell^1(s)$ is arens regular if and only if $s$ is finite.
We present a characterization of Arens regular semigroup algebras $\ell^1(S)$, for a large class of semigroups. Mainly, we show that if the set of idempotents of an inverse semigroup $S$ is finite, then $\ell^1(S)$ is Arens regular if and only if $S$ is finite.
In recent years there has been a growing number of constructions of faithful irreducible representations for the semigroup algebra FS of some specific inverse semigroups S. As usual, when S has a zero element θ, the contracted semigroup algebra F0S = FS/Fθ is considered. When F =
Let K be a commutative ring with unit and S an inverse semigroup. We show that the semigroup algebra KS can be described as a convolution algebra of functions on the universal étale groupoid associated to S by Paterson. This result is a simultaneous generalization of the author’s
Let R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R S is isomorphic to the direct product of Munn algebras M R GJ , mJ , nJ ;PJ with J ∈ S/J, where mJ is the number of R-classes in J , nJ the number of L-classes in J , a
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 $ninmath