共查询到20条相似文献,搜索用时 640 毫秒
1.
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an R-module M, we show that M is Gorenstein injective if and only if Hom
R
(Ȓ,M) belongs to Auslander category B(Ȓ), M is cotorsion and Ext
i
R
(E,M) = 0 for all injective R-modules E and all i > 0.
Received: 24 August 2006 Revised: 30 October 2006 相似文献
2.
Eero Hyry 《manuscripta mathematica》1999,98(3):377-390
Let A be a normal local ring which is essentially finite type over a field of characteristic zero. Let I⊂A 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
3.
Lutz Weis 《Mathematische Annalen》2001,319(4):735-758
We prove a Mihlin–type multiplier theorem for operator–valued multiplier functions on UMD–spaces. The essential assumption
is R–boundedness of the multiplier function. As an application we give a characterization of maximal –regularity for the generator of an analytic semigroup in terms of the R–boundedness of the resolvent of A or the semigroup .
Received July 19, 1999 / Revised July 13, 2000 / Published online February 5, 2001 相似文献
4.
This paper contains two theorems concerning the theory of maximal Cohen–Macaulay modules. The first theorem proves that certain
Ext groups between maximal Cohen–Macaulay modules M and N must have finite length, provided only finitely many isomorphism classes of maximal Cohen–Macaulay modules exist having ranks
up to the sum of the ranks of M and N. This has several corollaries. In particular it proves that a Cohen–Macaulay lo cal ring of finite Cohen–Macaulay type has
an isolated singularity. A well-known theorem of Auslander gives the same conclusion but requires that the ring be Henselian.
Other corollaries of our result include statements concerning when a ring is Gorenstein or a complete intersection on the
punctured spectrum, and the recent theorem of Leuschke and Wiegand that the completion of an excellent Cohen–Macaulay local
ring of finite Cohen–Macaulay type is again of finite Cohen–Macaulay type . The second theorem proves that a complete local
Gorenstein domain of positive characteristic p and dimension d is F-rational if and only if the number of copies of R splitting out of divided by has a positive limit. This result relates to work of Smith and Van den Bergh. We call this limit the F-signature of the ring and give some of its properties.
Received: 6 May 2001 / Published online: 6 August 2002
Both authors were partially supported by the National Science Foundation. The second author was also partially supported by
the Clay Mathematics Institute. 相似文献
5.
On Maximal Injectivity 总被引:5,自引:0,他引:5
Ming Yi WANG Guo ZHAO 《数学学报(英文版)》2005,21(6):1451-1458
A right R-module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R-homomorphism f : m → E can be extended to an R-homomorphism f^1 : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R-module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R-module over any left perfect right self-injective ring R is the injective hull of a projective submodule. 相似文献
6.
Hamidreza Rahmati 《Archiv der Mathematik》2009,92(1):26-34
A finite module M over a noetherian local ring R is said to be Gorenstein if Exti(k, M) = 0 for all i ≠ dim R. An endomorphism φ: R → R of rings is called contracting if for some i ≥ 1. Letting φR denote the R-module R with action induced by φ, we prove: A finite R-module M is Gorenstein if and only if HomR(φR, M) ≅ M and ExtiR(φR, M) = 0 for 1 ≤ i ≤ depth R.
Received: 7 December 2007 相似文献
7.
The paper considers linear independence measures of the values of certain q–hypergeometric series and their derivatives at algebraic points. The results are given both in the archimedean and p–adic case. 相似文献
8.
A. Mimouni 《manuscripta mathematica》2009,128(2):147-162
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
9.
We prove the versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring R of prime characteristic is regular if and only if for some proper ideal 𝔟 the derived local cohomology complex RΓ𝔟(R) has finite flat dimension when viewed through some positive power of the Frobenius endomorphism. 相似文献
10.
Manfred Knebusch 《Positivity》2007,11(4):639-686
Given a commutative ring A equipped with a preordering A+ (in the most general sense, see below), we look for a fractional ring extension (= “ring of quotients” in the sense of Lambek
et al. [L]) as big as possible such that A+ extends to a preordering R+ of R (i.e. with A ∩ R+ = A+) in a natural way. We then ask for subextensions A ⊂ B of A ⊂ R such that A is convex in B with respect to B+ : = B ∩ R+.
Supported by DFG.
A short form of this article has been delivered at the conference Carthapos 2006 at Carthago (Tunisia). 相似文献
11.
M.M. Cavalcanti V.N. Domingos Cavalcanti 《NoDEA : Nonlinear Differential Equations and Applications》2000,7(3):285-307
This paper is concerned to the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordon-Schr?dinger
damped equations
where ω is a bounded domain of R
n
, n≤ 3, F : R
2→R is a C
1-function; γ, β; θ are constants such that γ, β > 0 and 1 ≤ 2θ≤ 2.
Received January 1999 – Accepted October 1999 相似文献
12.
Shui Cao ZHENG Huo Nan LIN Di He HU 《数学学报(英文版)》2005,21(5):1137-1148
In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф(r) = r^N-d/α (log log l/r)d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d, α) strictly stable processes. 相似文献
13.
We show that under certain conditions on the topology of a faithful module M over a topological PI-ring R, if M has at most countable dual topological Krull dimension, then the closure of the sum of all Σ-nilpotent ideals of the ring
R is a Σ-nilpotent ideal too, and in the case of a bounded ring R its topological Baer radical is Σ-nilpotent.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 111–118, 2006. 相似文献
14.
In this paper, we prove the following theorem regarding the Wang–Yau quasi-local energy of a spacelike two-surface in a spacetime:
Let Σ be a boundary component of some compact, time-symmetric, spacelike hypersurface Ω in a time-oriented spacetime N satisfying the dominant energy condition. Suppose the induced metric on Σ has positive Gaussian curvature and all boundary
components of Ω have positive mean curvature. Suppose H ≤ H
0 where H is the mean curvature of Σ in Ω and H
0 is the mean curvature of Σ when isometrically embedded in
\mathbb R3{\mathbb R^3} . If Ω is not isometric to a domain in
\mathbb R3{\mathbb R^3}, then
1. |
the Brown–York mass of Σ in Ω is a strict local minimum of the Wang–Yau quasi-local energy of Σ. 相似文献
15.
Arrangements and cohomology 总被引:11,自引:0,他引:11
Michael Falk 《Annals of Combinatorics》1997,1(1):135-157
16.
In this article we study the common dynamics of two different Pisot substitutions σ
1 and σ
2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions
σ
1 and σ
2. Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function
systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems
which describe the common dynamics. We also consider generalizations of these results to the nonunimodular case, the case
of more than two substitutions and the case of two substitutions with different incidence matrices. 相似文献
17.
Simplice Tchamna Kouna 《代数通讯》2013,41(6):2513-2530
The ideal topology on a integral domain R is the linear topology which has as a fundamental system of neighborhoods of 0 the nonzero ideals of R. We investigate the properties of the ideal topology on a Noetherian local domain (R, 𝔪), and we establish connections between the 𝔪-adic completion and the ideal completion. We give conditions under which the completion in the ideal topology is Noetherian, and we show that, unlike the 𝔪-adic completion, the completion in the ideal topology is not always Noetherian. 相似文献
18.
When the role of network topology is taken into consideration, one of the objectives is to understand the possible implications of topological structure on epidemic models. As most real networks can be viewed as complex networks, we propose a new delayed SEτ IRωS epidemic disease model with vertical transmission in complex networks. By using a delayed ODE system, in a small-world (SW) network we prove that, under the condition R0 ≤ 1, the disease-free equilibrium (DFE) is globally stable. When R0 > 1, the endemic equilibrium is unique and the disease is uniformly persistent. We further obtain the condition of local stability of endemic equilibrium for R0 > 1. In a scale-free (SF) network we obtain the condition R1 > 1 under which the system will be of non-zero stationary prevalence. 相似文献
19.
We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example, as primal-dual conditions characterizing
solutions of optimization problems or variational inequalities. In particular, we discuss error bounds and Newton-type methods
for such systems. An exhaustive comparison of various regularity conditions which arise in this context is given. We obtain
a new error bound under an assumption which we show to be strictly weaker than assumptions previously used for KKT systems,
such as quasi-regularity or semistability (equivalently, the R
0-property). Error bounds are useful, among other things, for identifying active constraints and developing efficient local
algorithms. We propose a family of local Newton-type algorithms. This family contains some known active-set Newton methods,
as well as some new methods. Regularity conditions required for local superlinear convergence compare favorably with convergence
conditions of nonsmooth Newton methods and sequential quadratic programming methods.
Received: December 10, 2001 / Accepted: July 28, 2002 Published online: February 14, 2003
Key words. KKT system – regularity – error bound – active constraints – Newton method
Mathematics Subject Classification (1991): 90C30, 65K05 相似文献
20.
Thomas Marley 《manuscripta mathematica》2001,104(4):519-525
Let R be a commutative Noetherian local ring of dimension d, I an ideal of R, and M a finitely generated R-module. We prove that the set of associated primes of the local cohomology module H
i
I
(M) is finite for all i≥ 0 in the following cases: (1) d≤ 3; (2) d= 4 and $R$ is regular on the punctured spectrum; (3) d= 5, R is an unramified regular local ring, and M is torsion-free. In addition, if $d>0$ then H
d
− 1
I
(M) has finite support for arbitrary R, I, and M.
Received: 31 October 2000 / Revised version: 8 January 2001 相似文献
|