On generalized invariants of cyclic groups

Abstract

In this paper, we extend the definition of generalized invariants for any finite group. Further, we describe the structure of generalized invariants of a cyclic group for lower dimensional indecomposable representations in the modular case, where the characteristic of the ground field divides the group order. Finally, an analog of a conjecture about Hilbert ideals associated with invariant rings has been proven for the case of generalized invariants. (C) 2014 Elsevier B.V. All rights reserved.