2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142975Let p be an odd prime. We consider the cyclotomic extension T := Z_(p)[zeta_{p^2}] of S := Z_(p), with galois group G := (Z/p^2)^*. Since this extension is wildly ramified, the SG-module T is not projective. We calculate its cohomology ring H^*(G, T; S), carrying the cup product induced by the ring structure of T. Proceeding in a somewhat greater generality, our results also apply to certain Lubin-Tate extensions.Misprint in Th. 1.19 correctedNumber Theory11R33; 16S35text