Arens regularity of certain weighted semigroup algebras and countability (Q284676)

The authors first show that the Arens regularity of a weighted semigroup algebra is stable under certain homomorphisms of semigroups. Thus, they study those semigroups for which the Arens regularity of \(l_{1}(S,w)\) necessities the countability of \(S\). As the main result of this paper, they show that for a wide variety of semigroups the Arens regularity of \(l_{1}(S,w)\) implies that \(S\) is countable.