On the cyclotomic Dedekind embedding and the cyclic Wedderburn embedding

Details On the cyclotomic Dedekind embedding and the cyclic Wedderburn embedding On the cyclotomic Dedekind embedding and the cyclic Wedderburn embedding

2001-03-20

arxiv.org/abs/math/0103125v2

Alg. Rep. Th. 7, p. 211-259, 2004

Mathematics

Number Theory

minor corrections

Scientific paper

Let n >= 1 and let p be a prime. Let t = 1 - zeta_{p^n}. Expand an integer j in [0,p^n-1], coprime to p, p-adically as j = sum_{s >= 0} a_s p^s. 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] --> prod_{i in (Z/p^n)^*} Z_(p)[t] has valuation -1 + sum_{s >= 0} (a_s (s+1) - a_{s+1} (s+2)) p^s at t. There is a similar result for the related cyclic Wedderburn embedding.

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