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On regular local rings

open access: yesOn regular local rings
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On the fundamental theorem of regular local rings

open access: yesOn the fundamental theorem of regular local rings
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A REMARK ON THE HENSELIZATION OF A REGULAR LOCAL RING

Chinese Annals of Mathematics Series B, 1999
The author gives a characterization of the Henselization of an excellent regular local ring in terms of elements of the completion. Thus if \((R,m)\) is an excellent regular local with \(\widehat R\) as its completion, then an element \(a\) belongs to the Henselization \(\widetilde R\) if and only if there exists \(a b\) in \(\widehat R\) such that a \(
CARLOS Galindo
exaly   +3 more sources

p-BASIS OF A REGULAR SEMI-LOCAL RING

SUT Journal of Mathematics, 1995
On démontre la généralisation suivante d'un théorème donné aussi des mêmes auteurs [J. Math. Soc. Japan 34, 371-378 (1982; Zbl 0478.13009)]. Soient \(p > 0\) un nombre premier, \(R\) un anneau semilocal régulier de caractéristique \(p\) et \(R' \supseteq R^p\) un sous-anneau de \(R\) tel que \(R\) soit fini sur \(R'\).
KIMURA, Tetsuzo, NIITSUMA, Hiroshi
exaly   +3 more sources

Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring

open access: yesJournal of Pure and Applied Algebra, 2014
We prove that a quadratic A[T]-module Q with Witt index (Q/TQ)⩾d, where d is the dimension of the equicharacteristic regular local ring A, is extended from A.
Ravi A Rao
exaly   +2 more sources

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