A cancellation theorem for generalized Swan modules

Abstract

The module cancellation problem asks whether, given modules $X$, $X^{\prime }$ and $Y$ over a ring $\Lambda$, the existence of an isomorphism $X\oplus Y\cong X^{\prime }\oplus Y$ implies that $X\cong X^{\prime }$. When $\Lambda$ 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 $Y=\Lambda$ and $X$ is a generalized Swan module.