On cohomology rings of a cyclic group and a ring of integers

Abstract

We determine the ring homomorphism $H{H}^{*}(\Gamma )\to H^{*}(G,\Gamma )$ explicitly, where $G$ denotes the cyclic group of order $p^v$ and $\Gamma$ denotes the ring of integers of the cyclotomic field $\mathbb{Q}(\zeta )$ for a primitive $p^v$-th root of unity $\zeta$.