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On the fundamental theorem of regular local rings
On the fundamental theorem of regular local ringsopenaire
Combining Local and Von Neumann Regular Rings
Communications in Algebra, 2004 All rings R considered are commutative and have an identity element. Contessa called R a VNL-ring if a or 1 - a has a Von Neumann inverse whenever a ∈ R. Sample results: Every prime ideal of a VNL-ring is contained in a unique maximal ideal.
Osama Alkam
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NOTE ON INDECOMPOSABLE INTEGRALLY CLOSED MODULES OF RANK 2 OVER TWO-DIMENSIONAL REGULAR LOCAL RINGS
Journal of Commutative Algebra, 2023 We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank two.Comment: 6 ...
Vijay Kodiyalam
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Mathematika, 1956
In the following pages there will be found an account of the properties of a certain class of local rings which are here termed semi-regular local rings . As this name will suggest, these rings share many properties in common with the more familiar regular local rings, but they form a larger class and the characteristic properties are preserved under ...
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In the following pages there will be found an account of the properties of a certain class of local rings which are here termed semi-regular local rings . As this name will suggest, these rings share many properties in common with the more familiar regular local rings, but they form a larger class and the characteristic properties are preserved under ...
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Characterizations of Regular Local Rings of Characteristic p
American Journal of Mathematics, 1969exaly +2 more sources
Erratum to "Regular Overrings of Regular Local Rings"
Transactions of the American Mathematical Society, 1975THEOREM. Let (R, M) be an n-dimensional regular local ring, n > 1. Let x, xl, .. , xi be an R-sequence and T = R [xl/x, . . . , xi/x]. Then T is an ndimensional regular domain if and only if one of the following holds: (a) the elements x, x, ... , xi form a subset of a minimal basis for M, (b) (1) x E M2 and the elements xl, ...
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\(P\)-regular and \(P\)-local rings
2021Summary: This paper is a continuation of study rings relative to right ideal, where we study the concepts of regular and local rings relative to right ideal. We give some relations between \(P\)-local (\(P\)-regular) and local (regular) rings. New characterization obtained include necessary and sufficient conditions of a ring \(R\) to be regular, local
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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.
openaire +1 more source