Regularity of a Noetherian local ring with a p-basis

Mamoru Furuya; Takashi Yamaguchi

doi:10.55937/sut/1262445114

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Home > Journals > SUT J. Math. > Volume 42 > Issue 2 > Article

June 2006 Regularity of a Noetherian local ring with a

p

-basis

Mamoru Furuya, Takashi Yamaguchi

Author Affiliations +

Mamoru Furuya,¹ Takashi Yamaguchi¹
¹Department of Mathematics, Meijo University Shiogamaguchi, Tenpaku-ku, Nagoya, 468-8502, Japan

SUT J. Math. 42(2): 187-190 (June 2006). DOI: 10.55937/sut/1262445114

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Abstract

In this note, we shall show the following: Let $R$ be a Noetherian local ring of prime characteristic $p$ . If $R$ has a $p$ -basis over ${R^p}$ and $R$ is generically reduced, then $R$ is a regular local ring.

Acknowledgment

The authors thank the referee for careful reading and useful comments.

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Mamoru Furuya. Takashi Yamaguchi. "Regularity of a Noetherian local ring with a $p$ -basis." SUT J. Math. 42 (2) 187 - 190, June 2006. https://doi.org/10.55937/sut/1262445114