$\boldsymbol {m}$-adic $p$-basis and regular local ring
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- by Mamoru Furuya and Hiroshi Niitsuma PDF
- Proc. Amer. Math. Soc. 132 (2004), 3189-3193 Request permission
Abstract:
We introduce the concept of $\boldsymbol {m}$-adic $p$-basis as an extension of the concept of $p$-basis. Let $(S,\boldsymbol {m})$ 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 $\boldsymbol {m}$-adic $p$-basis of $S/R$ and $R$ is Noetherian.References
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Additional Information
- Mamoru Furuya
- Affiliation: Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku, Nagoya, 468-8502, Japan
- Email: furuya@ccmfs.meijo-u.ac.jp
- Hiroshi Niitsuma
- Affiliation: Faculty of Science, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan
- Email: niitsuma@rs.kagu.tus.ac.jp
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3189-3193
- MSC (2000): Primary 13H05, 13J10
- DOI: https://doi.org/10.1090/S0002-9939-04-07503-3
- MathSciNet review: 2073292