Projective covers of finitely generated Banach modules and the structure of some Banach algebras

Abstract

The investigation of the structure of biprojective Banach algebras with non-trivial radical forces the author to suppose that the idea of projective cover, which is important in Ring Theory, can be effectively applied to Banach algebras and modules. But, in fact, the structural results on biprojectivity can be easier obtained without projective covers, so there are no references to this matter in. Projective covers of Banach modules are considered in the present article. Except some assertions in Sections 1 and 6 we restrict our attention to the finitely generated case. The discussion concentrates on Banach algebras with conditions on the existence of projective covers.