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Discrete valuation ring - Definition, explanation In mathematics, a discrete valuation ring (DVR) is a particular kind of commutative ring that is a local ring, which satisfies conditions that in algebraic geometry come from non-singularity of a point on an algebraic curve. R is a noetherian local ring with positive Krull dimension, and the maximal ideal of R is principal. Any localization of a Dedekind domain is a discrete valuation ring; in practice, this is frequently how discrete valuation rings arise. www.calsky.com /lexikon/en/txt/d/di/discrete_valuation_ring.php   (280 words)

PlanetMath: discrete valuation Note: Discrete valuations are often written additively instead of multiplicatively; under this alternate viewpoint, the element It has the advantage that every valuation can be normalized by a suitable scalar multiple to take values in the integers. This is version 3 of discrete valuation, born on 2003-10-06, modified 2005-07-24. planetmath.org /encyclopedia/DiscreteValuation.html   (116 words)

Silberberg   (Site not responding. Last check: 2007-10-25) The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined. www.emis.de /journals/AM/00-2/silber.htm   (99 words)

PlanetMath: discrete valuation ring , and its value is independent of the choice of uniformizing element (Commutative rings and algebras :: Arithmetic rings and other special rings :: Valuation rings) (Commutative rings and algebras :: Local rings and semilocal rings :: Special types) planetmath.org /encyclopedia/Order6.html   (89 words)

Proceedings of the American Mathematical Society are constructed via categories of representations of antichains over discrete valuation rings. Descriptions and properties of modules in the images of these functors are given, including a characterization of finite representation type and a complete list of indecomposables in that case. D. Arnold, A duality for torsion-free modules of finite rank over a discrete valuation ring, Proc. www.ams.org /proc/2001-129-02/S0002-9939-00-05547-7/home.html   (382 words)

On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring (with Thomas Geisser) Let V be a discrete valuation ring of mixed characteristic (0,p) and let X be a smooth and proper scheme over V. We show that with Z/p www-math.mit.edu /~larsh/papers/012   (85 words)

Proceedings of the American Mathematical Society a complete discrete valuation ring with perfect residue field. I. Panin, On a theorem of Hurewicz and K-theory of complete discrete valuation rings, Math. J. Wagoner, Delooping the continuous K-theory of a valuation ring, Pacific J. Math. www.ams.org /joursearch/servlet/DoSearch?f1=msc&v1=11S70&jrnl=one&onejrnl=proc   (274 words)

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