共查询到20条相似文献，搜索用时 15 毫秒
1.
Rodney Y. Sharp 《Proceedings of the American Mathematical Society》2003,131(10):3009-3017
It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.
2.
In this paper we provide a complete characterization for when the Rees algebra and the associated graded ring of a perfect Gorenstein ideal of grade three are Cohen–Macaulay. We also treat the case of second analytic deviation one ideals satisfying some mild assumptions. In another set of results we give criteria for an ideal to be of linear type. Finally, we describe the equations defining the Rees algebras of certain Northcott ideals. 相似文献
3.
Y. Kinoshita K. Nishida Y. Yamanaka A. Yoneda 《Proceedings of the American Mathematical Society》2006,134(12):3437-3444
Let be a multiplicative filtration of a local ring such that the Rees algebra is Noetherian. We recall Burch's inequality for and give an upper bound of the a-invariant of the associated graded ring using a reduction system of . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension .
4.
In this article, we study the Castelnuovo–Mumford regularity and Gorenstein properties of the fiber cone. We obtain upper bounds for the Castelnuovo–Mumford regularity of the fiber cone and obtain sufficient conditions for the regularity of the fiber cone to be equal to that of the Rees algebra. We obtain a formula for the canonical module of the fiber cone and use it to study the Gorenstein property of the fiber cone. 相似文献
5.
In this article we introduce a certain family of graded modules associated to a given module. These modules provide a natural extension of the notion of the associated graded ring of an ideal. We will investigate their properties. In particular, we will try to extend Ree' theorem on the associated graded ring of an ideal generated by a regular sequence to this context. 相似文献
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7.
Shiro Goto Sin-Ichiro Iai Kei-ichi Watanabe 《Transactions of the American Mathematical Society》2001,353(6):2309-2346
Let be an -primary ideal in a Gorenstein local ring (, ) with , and assume that contains a parameter ideal in as a reduction. We say that is a good ideal in if is a Gorenstein ring with . The associated graded ring of is a Gorenstein ring with if and only if . Hence good ideals in our sense are good ones next to the parameter ideals in . A basic theory of good ideals is developed in this paper. We have that is a good ideal in if and only if and . First a criterion for finite-dimensional Gorenstein graded algebras over fields to have nonempty sets of good ideals will be given. Second in the case where we will give a correspondence theorem between the set and the set of certain overrings of . A characterization of good ideals in the case where will be given in terms of the goodness in their powers. Thanks to Kato's Riemann-Roch theorem, we are able to classify the good ideals in two-dimensional Gorenstein rational local rings. As a conclusion we will show that the structure of the set of good ideals in heavily depends on . The set may be empty if , while is necessarily infinite if and contains a field. To analyze this phenomenon we shall explore monomial good ideals in the polynomial ring in three variables over a field . Examples are given to illustrate the theorems.
8.
Shiro Goto Shin-ichiro Iai Mee-kyoung Kim 《Proceedings of the American Mathematical Society》2002,130(2):337-344
The structure of certain equimultiple good ideals in Gorenstein local rings obtained by idealization is explored.
9.
This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.
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11.
Summary LetR be a Cohen-Macaulay ring andI an unmixed ideal of heightg which is generically a complete intersection and satisfiesI
(n)=In for alln≥1. Under what conditions will the Rees algebra be Cohen-Macaulay or have good depth? A series of partial answers to this
question is given, relating the Serre condition (S
r
) of the associated graded ring to the depth of the Rees algebra. A useful device in arguments of this nature is the canonical
module of the Rees algebra. By making use of the technique of the fundamental divisor, it is shown that the canonical module
has the expected form: ω
R[It]
≅(t(1−t)
g−2).
The third author was partially supported by the NSF
This article was processed by the author using theLaTex style filecljour1 from Springer-Verlag. 相似文献
12.
We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question of Lorenz (1988).
13.
Erika Giorgi 《代数通讯》2013,41(8):2755-2767
Let A be a commutative Noetherian ring and I an ideal in A. We characterize algebraically when all the minimal primes of the associated graded ring G I A contract to minimal primes of A/I. This, applied to intersection theory, means that there are no embedded distinguished varieties of intersection. The characterization is in terms of the analytic spread of certain localizations of I, the symbolic Rees algebra, and the normalization of the Rees algebra, and extends results of Huneke, Vasconcelos, and Martí-Farré. 相似文献
14.
M. E. Rossi 《Proceedings of the American Mathematical Society》2000,128(5):1325-1332
Let be a local ring of positive dimension and let be an -primary ideal. We denote the reduction number of by , which is the smallest integer such that for some reduction of In this paper we give an upper bound on in terms of numerical invariants which are related with the Hilbert coefficients of when is Cohen-Macaulay. If , it is known that where denotes the multiplicity of If in Corollary 1.5 we prove where is the first Hilbert coefficient of From this bound several results follow. Theorem 1.3 gives an upper bound on in a more general setting.
15.
Mircea Cimpoeaş 《代数通讯》2013,41(2):724-727
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals. 相似文献
16.
Wolmer V. Vasconcelos> 《Compositio Mathematica》2003,139(3):361-379
Let (Rmbe 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. 相似文献
17.
Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. 相似文献
18.
Kuei-Nuan Lin 《代数通讯》2013,41(9):3673-3682
Abstract The notion of quasi-polynomials is very important in the theory of functional identities. For example, results on quasi-polynomials were tools in the solution of long-standing Herstein's Lie map conjectures. In this paper, we show that functional identities involving quasi-polynomial of degree one have only standard solutions on d-free sets. 相似文献
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20.
Shiro Goto Futoshi Hayasaka Shin-ichiro Iai 《Proceedings of the American Mathematical Society》2003,131(1):87-94
Let be a regular local ring and let be a filtration of ideals in such that is a Noetherian ring with . Let and let be the -invariant of . Then the theorem says that is a principal ideal and for all if and only if is a Gorenstein ring and . Hence , if is a Gorenstein ring, but the ideal is not principal.