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December 2020 Contracted Ideals of $p$-adic Integral Group Rings
Joongul LEE
Tokyo J. Math. 43(2): 529-536 (December 2020). DOI: 10.3836/tjm/1502179313

Abstract

Let $G$ be a cyclic group of order $p^k$ for a prime $p$. There is a natural embedding of $\mathbb{Z}_p[G]$ into a product of rings of integers of cyclotomic fields. We consider the ideals $I$ of $\mathbb{Z}_p[G]$ for which the following statement holds: if $\alpha\in\mathbb{Z}_p[G]$ and $\chi(\alpha)\in\chi(I)$ for all $p$-adic characters $\chi$ of $G$, then $\alpha\in I$. We show that they are precisely the contracted ideals of the embedding. Powers of the augmentation ideal of $\mathbb{Z}_p[G]$ are not contracted in general, and we calculate the obstruction of contraction in this case.

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Joongul LEE. "Contracted Ideals of $p$-adic Integral Group Rings." Tokyo J. Math. 43 (2) 529 - 536, December 2020. https://doi.org/10.3836/tjm/1502179313

Information

Published: December 2020
First available in Project Euclid: 20 July 2020

MathSciNet: MR4185847
Digital Object Identifier: 10.3836/tjm/1502179313

Subjects:
Primary: 16S34
Secondary: 20C05

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 2 • December 2020
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