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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


$\boldsymbol{\mathit{m}}$-adic $p$-basis and regular local ring

Authors: Mamoru Furuya and Hiroshi Niitsuma
Journal: Proc. Amer. Math. Soc. 132 (2004), 3189-3193
MSC (2000): Primary 13H05, 13J10
Published electronically: May 21, 2004
MathSciNet review: 2073292
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Abstract: We introduce the concept of $\boldsymbol{\mathit{m}}$-adic $p$-basis as an extension of the concept of $p$-basis. Let $(S,\boldsymbol{\mathit{m}})$ be a regular local ring of prime characteristic $p$ and $R$ a ring such that $S \supset R \supset S^p$. Then we prove that $R$ is a regular local ring if and only if there exists an $\boldsymbol{\mathit{m}}$-adic $p$-basis of $S/R$ and $R$ is Noetherian.

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Additional Information

Mamoru Furuya
Affiliation: Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku, Nagoya, 468-8502, Japan

Hiroshi Niitsuma
Affiliation: Faculty of Science, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

PII: S 0002-9939(04)07503-3
Keywords: $\boldsymbol{\mathit{m}}$-adic $p$-basis, regular local ring
Received by editor(s): January 29, 2003
Received by editor(s) in revised form: August 8, 2003
Published electronically: May 21, 2004
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society