Communications of the
Korean Mathematical Society CKMS

For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, 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 $l ^{1}(E)$-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 $\omega$.

Keywords: Banach modules, inverse semigroup, module Arens regularity, module amenability

MSC numbers: 43A10, 43A20, 46H20, 20M18