On the Cyclotomic Dedekind Embedding and the Cyclic Wedderburn Embedding期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the Cyclotomic Dedekind Embedding and the Cyclic Wedderburn Embedding

Authors:

Affiliation:

(1) Abt. Reine Mathematik, Universität Ulm, D-89069 Ulm, Germany;(2) Mathematisches Institut B, 3. Lehrstuhl, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Abstract:

Let n

1 and let p be a prime. Expand j isin

[0,pⁿ–1](p) p-adically as j= sum

_s0a_sp^s with a_s isin

[0,p–1]. The #([0,j](p))th Z_(p)[ zeta

_pⁿ]-linear elementary divisor of the cyclotomic Dedekind embedding

$Z_{(p)} [zeta _p ^n ] otimes _{Z_{(p)} } Z_{(p)} [zeta _p ^n ] to prodlimits_{i in left( {z/p_{}^n } right)^* } {Z_{(p)} } [zeta _p ^n ]$

has valuation

$- 1 + sumlimits_{s geqslant 0} {(a_s (s + 1) - a_{s + 1} (s + 2))} p^s$

at 1–

_pⁿ. There is a similar result for the related cyclic Wedderburn embedding.

Keywords:

cyclotomic extensions

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