Results 261 to 270 of about 48,395 (283)

The Core of a Module over a Two-Dimensional Regular Local Ring

Journal of Algebra, 1997
This paper explicitly determines the core of a torsion-free, integrally closed module over a two-dimensional regular local ring. It is analogous to a result of Huneke and Swanson which determines the core of an integrally closed ideal.
Mohan, Radha
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Semi‐regular local rings

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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Erratum to "Regular Overrings of Regular Local Rings"

Transactions of the American Mathematical Society, 1975
THEOREM. 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

2021
Summary: 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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Regular Local Rings

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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Wedderburn’s theorem for regular local rings

2015
Let \(R\) 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, 2000
Let \(R\) 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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On Locally Ιnvo-Regular Ring

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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Monoidal Transforms of Regular Local Rings

American Journal of Mathematics, 1973
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Polynomial rings and regular local rings

1993
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