P-ADIC ORDER BOUNDED GROUP VALUATIONS ON ABELIAN GROUPS

Abstract

AbstractFor a fixed integer e and prime p we construct the p-adic order bounded group valuations for a given abelian group G. These valuations give Hopf orders inside the group ring KG where K is an extension of $\mathbb{Q} _{p}$ with ramification index e. The orders are given explicitly when G is a p-group of order p or p2. An example is given when G is not abelian.