MODULE AMENABILITY AND MODULE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS

For every inverse semigroup S with subsemigroup E of idem-potents, necessary and sufficient conditions are obtained for the weighted semigroup algebra l(1) (S, omega) and its second dual to be l(1) (E)-module amen-ble. Some results for the module Arens regularity of l(1) (S, omega) (as an (1)(l) (E)-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that l(1) (S, omega) is module amenable but not amenable for any weight omega.