On the cyclotomic Dedekind embedding and the cyclic Wedderburn embedding
Harald Weber, Matthias Kuenzer
Abstract
Let n >= 1 and let p be a prime. Let t = 1 - zetapn. Expand an integer j in [0,pn-1], coprime to p, p-adically as j = sums >= 0 as ps. Denote the tensor product over Z(p) by o . Then the #([0,j] - (p))th Z(p)[t]-linear elementary divisor of the cyclotomic Dedekind embedding Z(p)[t] o Z(p)[t] --> prodi in (Z/pn)* Z(p)[t] has valuation -1 + sums >= 0 (as (s+1) - as+1 (s+2)) ps at t. There is a similar result for the related cyclic Wedderburn embedding.
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