in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

The cohomology of a group G with coefficients in a left G–module M is denoted H .GIM /. We are primarily interested in the case where M is the group ring, ZG . Since ZG is a G–bimodule, H .GIZG/ inherits the structure of a right G– module. When G is discrete and acts properly and cocompactly on a contractible CW complex , there is a natural topological interpretation for this cohomology group:...

A unital Fréchet algebra A is called contractible if there exists an element d ∈ A⊗̂A such that πA(d) = 1 and ad = da for all a ∈ A where πA : A⊗̂A → A is the canonical Fréchet A-bimodule morphism. We give a sufficient condition for an infinite-dimensional contractible Fréchet algebra A to be a direct sum of a finite-dimensional semisimple algebra M and a contractible Fréchet algebra N without an...