منابع مشابه
Multiplicities and Rees Valuations
Let (R, m) be a local ring of Krull dimension d and I ⊆ R be an ideal with analytic spread d. We show that the j-multiplicity of I is determined by the Rees valuations of I centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an O(nd) rate.
متن کاملRees Valuations
This expository paper contains history, definitions, constructions, and the basic properties of Rees valuations of ideals. A section is devoted to one-fibered ideals, that is, ideals with only one Rees valuation. Cutkosky [5] proved that there exists a two-dimensional complete Noetherian local integrally closed domain in which no zero-dimensional ideal is one-fibered. However, no concrete ring ...
متن کاملPommaret Bases and Rees Decomposition
We define involutive bases for polynomial ideals and demonstrate their use in calculating direct decompositions of polynomial modules, focusing on the so-called Pommaret bases. The resulting decomposition is the well known Rees decomposition. An overview of other important applications of Pommaret bases is given.
متن کاملRees products and lexicographic shellability
We use the theory of lexicographic shellability to provide various examples in which the rank of the homology of a Rees product of two partially ordered sets enumerates some set of combinatorial objects, perhaps according to some natural statistic on the set. Many of these examples generalize a result of J. Jonsson, which says that the rank of the unique nontrivial homology group of the Rees pr...
متن کاملMultiplicities and Reduction Numbers
Let (R,m) be a Cohen–Macaulay local ring and let I be an ideal. There are at least five algebras built on I whose multiplicity data affect the reduction number r(I) of the ideal. We introduce techniques from the Rees algebra theory of modules to produce estimates for r(I), for classes of ideals of dimension one and two. Previous cases of such estimates were derived for ideals of dimension zero.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Collectanea mathematica
سال: 2010
ISSN: 0010-0757
DOI: 10.1007/bf03191222