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 -adic  -basis and regular local ring |
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| Authors: | Mamoru Furuya Hiroshi Niitsuma |
| Affiliation: | Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku, Nagoya, 468-8502, Japan ; Faculty of Science, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan |
| Abstract: | We introduce the concept of  -adic  -basis as an extension of the concept of  -basis. Let  be a regular local ring of prime characteristic  and  a ring such that  . Then we prove that  is a regular local ring if and only if there exists an  -adic  -basis of  and  is Noetherian. |
| Keywords: | $boldsymbol{mathit{m}}$-adic $p$-basis regular local ring |
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