𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multiplicities and a Dimension Inequality for Unmixed Modules

✍ Scribed by Sean Sather-Wagstaff

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
137 KB
Volume
238
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We prove the following result, which is motivated by the recent work of Kurano and Roberts on Serre's positivity conjecture. Assume that R is a local ring with finitely generated module M such that R/Ann M is quasi-unmixed and contains a field, and that and are prime ideals in the support of M such that is analytically unramified, √ + = and e M = e M . Then

We also prove a similar theorem in a special case of mixed characteristic. Finally, we provide several examples to explain our assumptions as well as an example of a noncatenary local domain R with prime ideal such that e R p > e R = 1.

πŸ“œ SIMILAR VOLUMES

Inequalities for a Weighted Multiple Int
Inequalities for a Weighted Multiple Integral
✍ Feng Qi πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 71 KB

In the article, using Taylor's formula for functions of several variables, the author establishes some inequalities for the weighted multiple integral of a function defined on an m-dimensional rectangle, if its partial derivatives of Ε½ . n q 1 th order remain between bounds. Using this result, Iyeng

Existence and multiplicity results for q
Existence and multiplicity results for quasilinear hemivariational inequalities at resonance
✍ Leszek GasiΕ„ski πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 204 KB

## Abstract In this paper we consider quasilinear hemivariational inequality at resonance. We prove existence results for strongly resonant quasilinear problem, resonant problem under a Tang‐type condition as well as two multiplicity results. The method of the proofs is based on the nonsmooth criti

Multiple Solutions for a Class of Hemiva
Multiple Solutions for a Class of Hemivariational Inequalities Involving Periodic Energy Functionals
✍ D. Goeleven; D. Motreanu; P. D. Panagiotopoulos πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 346 KB πŸ‘ 2 views

In this paper we prove firstly that if f : XP1 is a locally Lipschitz function, bounded from below and invariant to a discrete group of dimension N is a suitable sense, acting on a Banach space X, then the problem: find u 3X such that o3 j f (u) (here j f (u) denotes Clarke's generalized gradient o