by Künzer, M.; Weber, H.

Let n≥1 and let p be a prime. Expand j∈[0,p

ⁿ
−1]\(p) p-adically as j=∑
_s≥0
a

_s

p

^s
with a

_s
∈[0,p−1]. The #([0,j]\(p))th
_(p)[ζ
_p


ⁿ
]-linear elementary divisor of the cyclotomic Dedekind embedding
$$Z_{(p)} [\zeta _p ^n ] \otimes _{Z_{(p)} } Z_{(p)} [\zeta _p ^n ] \to \prod\limits_{i \in \left( {z/p_{}^n } \right)^* } {Z_{(p)} } [\zeta _p ^n ]$$
has valuation
$$ – 1 + \sum\limits_{s \geqslant 0} {(a_s (s + 1) – a_{s + 1} (s + 2))} p^s $$
at 1−ζ
_p


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

DOI: 10.1023/B:ALGE.0000031024.07375.75
Print publication date: 8/1/2004
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