Module contractibility for semigroup algebras

Abstract

In this paper, we nd the relationships between module contractibility of a<br />Banach algebra and its ideals. We also prove that module contractibility of<br />a Banach algebra is equivalent to module contractibility of its module uniti-<br />zation. Finally, we show that when a maximal group homomorphic image of<br />an inverse semigroup S with the set of idempotents E is nite, the module<br />projective tensor product l¹(S)×_l¹(E)l¹(S) is l¹(E)-module contractible.