Weak module amenability of module extension Banach algebras

In this paper, we study module and weak module amenability of the module extension Banach algebra A⊕X of a Banach algebra A by a Banach A-module X. As an example, we show that for an inverse semigroup S with set of idempotents E, the module extension l۱(E)⊕l۱(S) is amenable as an l۱(E)-module if and only if S is amenable. We also study module biflatness and module biprojectivity of module extensions.

کلیدواژه ها:

Semigroup algebras ، Weak module amenability