共查询到20条相似文献,搜索用时 15 毫秒
1.
Duong Quô c Vi d ê t 《Proceedings of the American Mathematical Society》2008,136(12):4185-4195
Let be a Noetherian local ring with the maximal ideal and an ideal of Denote by the fiber cone of This paper characterizes the multiplicity and the Cohen-Macaulayness of fiber cones in terms of minimal reductions of ideals.
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Let (R, m) be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal (almost minimal) mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones. 相似文献
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Let (R,m) be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ? 1 and λ( JKKIIkk-1 ) = 1. We show that if depth G(I) ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK(I) assuming that depth G(I) ≥ d - 1. 相似文献
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The paper characterizes the length of maximal sequences satisfying conditions (i) and (ii) of (FC)-sequences, and proves some properties of (FC)-sequences, such as a bound on their lengths. As a consequence we get some results for mixed multiplicities and multiplicities of Rees rings of equimultiple ideals. We also prove that if is an ideal of positive height and is an arbitrary maximal sequence in satisfying conditions (i) and (ii) of (FC)-sequences, then is a reduction of
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Guangjun Zhu 《代数通讯》2013,41(10):3686-3696
Let (R, 𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When r(I | K)<∞, we give a lower bound and an upper bound for f 1(I). Under the above assumption on r(I | K) and depth G(I) ≥ d ? 1, we also provide a characterization, in terms of f 1(I), of the condition depth F K (I) ≥ d ? 1. 相似文献
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Let (R, 𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R and K an ideal containing I. When depth G(I) ≥ d ? 1 and r(I | K) < ∞, we present a lower bound on the second fiber coefficient of the fiber cones, and also provide a characterization, in terms of f 2(I, K), of the condition depth F K (I) ≥ d ? 1. 相似文献
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《代数通讯》2013,41(7):3529-3546
Abstract For an ideal I of a Noetherian local ring (R, m ) we consider properties of I and its powers as reflected in the fiber cone F(I) of I. In particular,we examine behavior of the fiber cone under homomorphic image R → R/J = R′ as related to analytic spread and generators for the kernel of the induced map on fiber cones ψ J : F R (I) → F R′(IR′). We consider the structure of fiber cones F(I) for which ker ψ J ≠ 0 for each nonzero ideal J of R. If dim F(I) = d > 0,μ(I) = d + 1 and there exists a minimal reduction J of I generated by a regular sequence,we prove that if grade(G +(I)) ≥ d ? 1,then F(I) is Cohen-Macaulay and thus a hypersurface. 相似文献
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A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(gl) of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V (λ) as a U(gl)-module into a direct sum of Weyl modules V (μ)’s as U(gl-1)modules is described. In particular, a new multiplicity formula for the Weyl module V (λ) is obtained in this note. 相似文献
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In this paper we present some new and pertinent connections between the Strong Optimization and the Approximate Pareto type
Efficiency, in particular, with the usual Vector Optimization, at first in the Ordered Vector Spaces by the natural Convex
Cones and, afterwards, in the Ordered Hausdorff Locally Convex Spaces. The main result is obtained considering the notion
of full nuclear cone. Our results, is related to an appropriate scalarization method
Mathematics Subject Classification (2000). 90C29 相似文献
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Philip Korman 《Mathematische Nachrichten》2001,229(1):119-127
We study uniqueness and exact multiplicity of solutions of semilinear equations for both balls and annular domains. We assume the annular domains to be “thin ”, but allow them to be wider than in the previous works. 相似文献
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Bernd Ulrich Wolmer V. Vasconcelos 《Transactions of the American Mathematical Society》2005,357(2):425-442
The computation of the integral closure of an affine ring has been the focus of several modern algorithms. We will treat here one related problem: the number of generators the integral closure of an affine ring may require. This number, and the degrees of the generators in the graded case, are major measures of cost of the computation. We prove several polynomial type bounds for various kinds of algebras, and establish in characteristic zero an exponential type bound for homogeneous algebras with a small singular locus.
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局部β-凸空间的共轭锥与Hahn-Banach定理 总被引:4,自引:1,他引:4
王见勇 《数学的实践与认识》2002,32(1):143-149
由 [1 ],局部β-凸空间 X的共轭锥 X*β 取代共轭空间在局部β-凸分析中扮演核心角色 .本文第一部分在局部β-凸空间上给出β-次半范的 Hahn-Banach定理 ,第二部分通过共轭锥 ( X*β ,‖‖ )得到赋β-范空间 ( X,‖‖β)的可分性定理 ,第三部分给出局部 β-凸空间的共轭锥 X*β 在一致收敛拓扑下的完备性定理等 . 相似文献
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We study the asymptotic behavior of the maximal multiplicity μn = μn(λ) of the parts in a partition λ of the positive integer n, assuming that λ is chosen uniformly at random from the set of all such partitions. We prove that πμn/(6n)1/2 converges weakly to max jXj/j as n→∞, where X1, X2, … are independent and exponentially distributed random variables with common mean equal to 1.2000 Mathematics Subject Classification: Primary—05A17; Secondary—11P82, 60C05, 60F05 相似文献
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本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥Tkσ(x)的直接像,弱相依导数DσF(x,y)的一个链式法则以及偏y弱导数DyσF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数DσF(x,y)及弱P导数PσF(x,y)判定无穷维 相似文献
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Indah Emilia Wijayanti 《代数通讯》2013,41(4):1308-1333
Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C* is prime. This definition, however, is not intrinsic—it strongly depends on the base ring being a field. The purpose of the article is to provide a better understanding of related notions for coalgebras over commutative rings by employing traditional methods from (co)module theory, in particular (pre)torsion theory. Dualizing classical primeness condition, coprimeness can be defined for modules and algebras. These notions are developed for modules and then applied to comodules. We consider prime and coprime, fully prime and fully coprime, strongly prime and strongly coprime modules and comodules. In particular, we obtain various characterisations of prime and coprime coalgebras over rings and fields. 相似文献
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Mathematical Notes - 相似文献