Algebras With Vanishing n-Cohomology Groups

Abstract

Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.