Some Remarks on the Tensor Product of Algebras and Applications II

Abstract

We apply the G-algebra theory to the tensor product of algebras. These considerations are applied to extend the results of Alghamdi and Khammash [1], Khammash [4] and Külshammer [5, Proposition 1.2] on the tensor product of group algebras and modules over an algebraically closed field to lattices over a complete discrete valuation ring. This places these results in the standard integral finite group modular representation theory of G-algebras as pioneered by Puig (cf. [8]). We also study some aspects of covering homomorphisms and the Green correspondence in this context (cf. [8, Sections 20 and 25]).