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A REMARK ON THE HENSELIZATION OF A REGULAR LOCAL RING
Chinese Annals of Mathematics, 1999The 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 \(
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p-BASIS OF A REGULAR SEMI-LOCAL RING
SUT Journal of Mathematics, 1995On 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
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2010
As mentioned before, local rings serve for the study of the local behavior of a global object, such as an affine variety. In particular, notions of local “niceness” can be defined as properties of local rings. There is a range of much-studied properties of local rings.
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As mentioned before, local rings serve for the study of the local behavior of a global object, such as an affine variety. In particular, notions of local “niceness” can be defined as properties of local rings. There is a range of much-studied properties of local rings.
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Wedderburn’s theorem for regular local rings
2015Let \(R\) be a regular local ring containing a field of characteristic zero, \(K\) its field of fractions and \((V, \Phi)\) a quadratic space over \(R\). \textit{I. Panin} proved that if \((V, \Phi) \otimes_RK\) is isotropic over \(K\), then \((V, \Phi)\) is isotropic over \(R\) [Invent. Math. 176, No. 2, 397--403 (2009; Zbl 1173.11025)].
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Cofiniteness of Local Cohomology Modules Over Regular Local Rings
Bulletin of the London Mathematical Society, 2000Let \(R\) be a regular local ring of Krull dimension \(d\), \(I\) a 1-dimensional ideal of it and \(M\) a finitely generated \(R\)-module. In this paper we give a new proof of the fact that the local cohomology modules \(H^i_I(M)\) are \(I\)-cofinite, that is, \(\text{Ext}^i_R(R/I, H^i_I(M))\) are finitely generated for all \(i,j\geq 0\). The hard part
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Advances in Nonlinear Variational Inequalities
An associative ring with identity D claimed to be locally Invo- regular ( L.Ι.Reg.Rings) if , for any element ӻ in D , either ӻ or 1- ӻ is Invo-regular in D , that is ӻ = ӻ v ӻ or 1- ӻ = (1- ӻ) v (1- ӻ) for some involution element v in D , these rings due to Danchev [5] .
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An associative ring with identity D claimed to be locally Invo- regular ( L.Ι.Reg.Rings) if , for any element ӻ in D , either ӻ or 1- ӻ is Invo-regular in D , that is ӻ = ӻ v ӻ or 1- ӻ = (1- ӻ) v (1- ӻ) for some involution element v in D , these rings due to Danchev [5] .
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Regular bi-interpretability of Chevalley groups over local rings
European Journal of Mathematics, 2023exaly
Monoidal Transforms of Regular Local Rings
American Journal of Mathematics, 1973openaire +2 more sources
Differential Simplicity in Regular Local Rings
Bulletin of the London Mathematical Society, 1978openaire +2 more sources
Extensions and Simplifications of the Theory of Regular Local Rings
Journal of the London Mathematical Society, 1957Northcott, D. G., Rees, D.
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