A cancellation theorem for generalized Swan modules

Abstract

The module cancellation problem asks whether, given modules X, X′ and Y over a ring Λ, the existence of an isomorphism X⊕Y≅X′⊕Y implies that X≅X′. When Λ is the integral group ring of a metacyclic group G(p,q), results of Klingler show that the answer to this question is generally negative. By contrast, in this case we show that cancellation holds when Y=Λ and X is a generalized Swan module.