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1.
Résumé  Une extensionA⊂B des anneaux (commutatifs) satisfait à la propriété si tout arbre dans Spec(B) couvre un arbre dans Spec(A). Il est possible qu'une extension entière d'un anneau Noethérien ne satisfait pas à . SiA⊂B soit unei-extension satisfaisante à soit “going-up” soit “going-down”, alorsA⊂B satisfait à . Cependant, une extension d'anneaux satisfaisante à “going-up”, “going-down”, et peut être nonunibranche dans hauteur >1. Un anneau intègreA a le spectre d'un arbre si et seulement siA⊂B satisfait àP pour tout anneau intègreB contenantA (resp., suranneau de BézoutB deA). De plus, si un anneau intègreA n'ait pas de spectre d'un arbre mais soit localement de dimension finie, (par exemple, tout anneau intègre Noethérien de dimension au moins 2), alors il existe un suranneau de BézoutB deA et un arbre saturé dans Spec(B) de sorte que card=4 et l'image de à l'égard de la flèche canonique Spec(B)→Spec(A) est un ensemble saturé tel que card =3 mais n'est pas d'arbre. On donne également des caractérisations associées des classes desi-domaines et des ai-domaines.   相似文献   

2.
SoientAB des anneaux (commutaifs et unitaires). On dit que (A,B) est une paire d’anneaux de going-down siD est un anneau de going-down pour tout anneauD tel queADB. On preuve que (A,B) est une paire d’anneaux de going-down si et seulement siA[b 1,b 2] est un anneau de going-down pour toutb 1,b 2 εB.  相似文献   

3.
For a Gaussian prime (i) define ()=min|–| where runs through Gaussian primes satisfying ||>||. We prove that, subject to the Riemann Hypothesis for appropriateL-functions
which generalises a result due to Selberg (Archiv for Mathematik og Naturvidenskab47 (1943) 87–105).  相似文献   

4.
We compute some algebraic invariants (e.g. depth, Castelnuovo-Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products. Received: 25 October 2007  相似文献   

5.
Let R be an integral domain with quotient field L. An overring T of R is t-linked over R if I −1 = R implies that (T : IT)  =  T for each finitely generated ideal I of R. Let O t (R) denotes the set of all t-linked overrings of R and O(R) the set of all overrings of R. The purpose of this paper is to study some finiteness conditions on the set O t (R). Particularly, we prove that if O t (R) is finite, then so is O(R) and O t (R) = O(R), and if each chain of t-linked overrings of R is finite, then each chain of overrings of R is finite. This yields that the t-linked approach is more efficient than the Gilmer’s treatment (Proc Am Math Soc 131:2337–2346, 2002). We also examine the finiteness conditions in some Noetherian-like settings such as Mori domain, quasicoherent Mori domain, Krull domain, etc. We establish a connection between O t (R) and the set of all strongly divisorial ideals of R and we conclude by a characterization of domains R that are t-linked under all their overrings. This work was funded by KFUPM under Project # FT/18-2005.  相似文献   

6.
Résumé  On dit qu'un anneau intègreR est fragmenté si pour tout élément non-inversibler deR, il existe un élément non-inversibles deR tel que r∈∩Rs n. On montre, pour un anneau intègreR qui n'est pas un corps, qu'il existe un idéal maximal deR qui contient une cha?ne strictement croissante d'idéaux premiers deR. Si, de plus,R n'ax qu'un nombre fini d'idéaux maximaux, alors on peut reformuler l'affirmation précédente pour tout idéal maximal deR. Il découle que toute anneau intègreR, qui n'est pas un corps et qui possède un idéal premierP tel queR+PR p soit fragmenté, doit être de dimension infinie (au sens de Krull). On donne un exemple d'un tel anneauR qui n'est pas fragmenté.   相似文献   

7.
It is well-known that ifX is a compact metric space and ifI is a capacity onX then every analytic subset ofX isI-capacitable [2], [1]. We introduce the notion of vector-valued capacity in the case when the codomain is a Banach lattice and we prove an analogous theorem for analytic subsets of a Polish space. Finally, we show that every vectorvalued outer measure is a capacity and, in connection with the so-called “marginal problem”, we give an example of a capacity taking values in a reflexive Banach lattice.  相似文献   

8.
We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming. Dedicated to Professor Toshiyuki Katsura on the occasion of his sixtieth birthday  相似文献   

9.
Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let IA be an ideal such that the Rees algebra R A (I) is Cohen–Macaulay and normal. In this paper we address the question: “When does R A (I) have rational singularities?” In particular, we study the connection between rational singularities of R A (I) and the adjoint ideals of the powers I n (n∋ℕ). Received: 25 May 1998 / Revised version: 20 August 1998  相似文献   

10.
A new Cauchy-type formula for hypermonogenic functions is derived. Hypermonogenic functions, introduced in [6], are a generalization of holomorphic functions to several dimensions. The power function xm is hypermonogenic. This paper is dedicated to the memory of our friend and colleague Jarolim Bureš  相似文献   

11.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on . Received: October, 2007. Accepted: February, 2008.  相似文献   

12.
We consider a finite dimensional k-algebraA and associate to each tilting module a cone in the Grothendieck groupK 0 of finitely generated A-modules. We prove that the set of cones associated to tilting modules of projective dimension at most one defines a, not necessarily finite, fan Σ(A). IfA is of finite global dimension, the fan Σ(A) is smooth. Moreover, using the cone of a tilting module, we can associate a volume to each tilting module. Using the fan and the volume, we obtain new proofs for several classical results; we obtain certain convergent sums naturally associated to the algebraA and obtain criteria for the completeness of a list of tilting modules. Finally, we consider several examples. Dedicated to O. Riemenschneider on the occasion of his 65th birthday  相似文献   

13.
This article is about the accurate computation of the eigenvalues of nonnormal tridiagonal matrices. Results of a comparison we made between several methods and algorithms are reported, and an algorithm derived from the method presented in [15], [16] is shown to be the only one able to give accurate outputs in case of ill-conditioned eigenvalues.
Conferenza tenuta da L. Pasquini il 29 maggio 1995  相似文献   

14.
Let
I m is the identity matrix of order m. Let W(λ) be an entire matrix valued function of order 2m, W(0) = I 2m , the values of W(λ) are j mm -unitary at the imaginary axis and strictly j mm -expansive in the open right half-plane. The blocks of order m of the matrix W(λ) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any λ with positive real part this equation has a unique contractive solution θ(λ). The matrix valued function θ(λ) can be represented in a form θ(λ) = θ A (iλ) where θ A (μ) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form
with periodic coefficients.  相似文献   

15.
This paper is devoted to a practical formula for computing e tA, where A is anr×r matrix. Our main result is based on the combinatorial aspect of generalized Fibonacci sequences. Examples and applications are given. Date: June 9, 2003.  相似文献   

16.
We show that given any Borel measure onR, every Lipschitz function is μ-a.e. differentiable with respect to μ.  相似文献   

17.
It is observed that the additive as well as multiplicative Jordan decompositions hold in alternative loop algebras of finiteRA loops and theRA loops for which the additive Jordan decomposition holds in the integral loop ring are characterized. Multiplicative Jordan decomposition (MJD) inZL, whereL is a finiteRA loop with cyclic centre is analysed, besides settling MJD for integral loop rings of allRA loops of order ≤32. It is also shown that for any finiteRA loopL,U (ZL) is an almost splittable Moufang loop. Research of the second author is supported by CSIR.  相似文献   

18.
In this paper we are working with a generalized Kolosov-Muskhelishvili formula. This representation formula expresses the elastic displacements of a solid body in terms of two monogenic functions. Known polynomial systems of monogenic functions are used to construct a basis of polynomial solutions to the Lamé system from linear elasticity. Received: October, 2007. Accepted: February, 2008.  相似文献   

19.
In this article we consider Riemann surfacesF of genus g ≥ 0 with n ≥ 1 incoming and m ≥ 1 outgoing boundary circles, where on each incoming circle a point is marked. For the moduli space mg*(m, n) of all suchF of genusg ≥ 0 a configuration space model Radh(m, n) is described: it consists of configurations of h = 2g-2+m+n pairs of radial slits distributed over n annuli; certain combinatorial conditions must be satisfied to guarantee the genusg and exactly m outgoing circles. Our main result is a homeomorphism between Radh(m, n) and Mg*(m,n). The space Radh(m, n) is a non-compact manifold, and the complement of a subcomplex in a finite cell complex. This can be used for homological calculations. Furthermore, the family of spaces Radh(m, n ) form an operad, acting on various spaces connected to conformai field theories.  相似文献   

20.
In this paper we to define and study a class of metric continua called ultra smooth, which (by the definition) form a subclass of the class of continua being hereditarily unicoherent at some point. The major result is that every ultra smooth continuum is smooth.  相似文献   

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