Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on regularity of Noetherian complete local rings of unequal characteristic

Mamoru Furuya and Hiroshi Niitsuma

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Let $(R, \boldsymbol{m})$ be a Noetherian complete local ring with unequal characteristic, and let $(P, pP)$ be a discrete valuation ring contained in $R$. Then, under some assumptions of separability on the residue fields, the following conditions are equivalent: (1) $R$ is a regular local ring and $p \notin \boldsymbol{m}^2$. (2) The $\boldsymbol{m}$-adic higher differential algebra $\widehat{D}_t(R/P, \boldsymbol{m})$ is a polynomial ring over $R$ for some $t~(1 \leq t)$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 8 (2002), 166-168.

First available in Project Euclid: 23 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Secondary: 13H05: Regular local rings

Regular local ring $\boldsymbol {m}$-adic higher differential algebra


Furuya, Mamoru; Niitsuma, Hiroshi. A note on regularity of Noetherian complete local rings of unequal characteristic. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 8, 166--168. doi:10.3792/pjaa.78.166.

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