MODULE AMENABILITY AND MODULE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS

Abstract

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra l1(S, ω) and its second dual to be l1(E)-module amenble. Some results for the module Arens regularity of l1(S, ω) (as an l1(E)module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that l1(S, ω) is module amenable but not amenable for any weight ω.