Calculations of Tensor Products Over Modular Representations in Characteristic P

Abstract

In papers by J.A. Green and R.-C. Renaud indecomposable modules of cyclic groups of prime power order are studied through the use of tensor products, as well as the characters on these modules. In this paper I will exhibit two decompositions, one for the product of any two indecomposable modules as a sum, and another for any single module as a product of basis elements. This will allow for easy computation of the character known as the Frobenius Perron dimension.