A STRONG CANCELLATION THEOREM FOR MODULES OVER C∞×Cq

Abstract

The module cancellation problem asks whether, given modules $X$, $X^{\prime }$ and $Y$ over a ring $\mathrm{\Lambda }$, the existence of an isomorphism $X\oplus Y\cong X^{\prime }\oplus Y$ implies that $X\cong X^{\prime }$. When $q$ is prime we prove a strong cancellation property for certain modules over $\mathbb{Z}[C_{\infty }\times C_q]$, generalizing, in part, the strong cancellation property for modules over $\mathbb{Z}[C_q]$ established by R. Wiegand (1984).