Abstract
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 $t~(1 \leq t)$.
Citation
Mamoru Furuya. Hiroshi Niitsuma. "A note on regularity of Noetherian complete local rings of unequal characteristic." Proc. Japan Acad. Ser. A Math. Sci. 78 (8) 166 - 168, Oct. 2002. https://doi.org/10.3792/pjaa.78.166
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