共查询到20条相似文献,搜索用时 15 毫秒
1.
The study of maximal-primary irreducible ideals in a commutative graded connected Noetherian algebra over a field is in principle equivalent to the study of the corresponding quotient algebras. Such algebras are Poincaré duality algebras. A prototype for such an algebra is the cohomology with field coefficients of a closed oriented manifold. Topological constructions on closed manifolds often lead to algebraic constructions on Poincaré duality algebras and therefore also on maximal-primary irreducible ideals. It is the purpose of this note to examine several of these and develop some of their basic properties. 相似文献
2.
Goto numbers for certain parameter ideals Q in a Noetherian local ring (A,m) with Gorenstein associated graded ring are explored. As an application, the structure of quasi-socle ideals I=Q:mq (q≥1) in a one-dimensional local complete intersection and the question of when the graded rings are Cohen-Macaulay are studied in the case where the ideals I are integral over Q. 相似文献
3.
V. Bonanzinga 《Archiv der Mathematik》2003,81(4):385-396
In this paper we characterize all principal Borel ideals with Borel generator
up to degree 4 which are Gotzmann. We also classify principal Borel ideals with a
Borel generator of degree d which are lexsegment
and we describe the shadows of principal Borel ideals. Finally, we
discuss the corresponding results for squarefree monomial ideals.Received: 10 May 2002 相似文献
4.
This paper explores the structure of quasi-socle ideals I=Q:m2 in a Gorenstein local ring A, where Q is a parameter ideal and m is the maximal ideal in A. The purpose is to answer the problems as to when Q is a reduction of I and when the associated graded ring is Cohen-Macaulay. Wild examples are explored. 相似文献
5.
We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral closure of an ideal. We start by giving a new geometric interpretation of the Reid–Roberts–Singh criterion for when an element is weakly subintegral over a subring. We give new characterizations of the weak subintegral closure of an ideal. We associate with an ideal I of a ring A an ideal I>, which consists of all elements of A such that v(a)>v(I), for all Rees valuations v of I. The ideal I> plays an important role in conditions from stratification theory such as Whitney's condition A and Thom's condition Af and is contained in every reduction of I. We close with a valuative criterion for when an element is in the weak subintegral closure of an ideal. For this, we introduce a new closure operation for a pair of modules, which we call relative weak closure. We illustrate the usefulness of our valuative criterion. 相似文献
6.
Kathrin Kuhnigk 《Journal of Pure and Applied Algebra》2007,210(2):473-480
In this note we present some computational tools to aide in the determination of Macaulay inverses of Hilbert ideals of finite groups and related ideals. 相似文献
7.
Michael Dokuchaev 《Journal of Pure and Applied Algebra》2007,208(1):77-87
In this article, among other results, we develop a Galois theory of commutative rings under partial actions of finite groups, extending the well-known results by S.U. Chase, D.K. Harrison and A. Rosenberg. 相似文献
8.
Among the several types of closures of an idealI that have been defined and studied in the past decades, the integral closureĪ has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to
describe it concretely once the generators ofI are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing
for integral closedness, and in caseI ≠Ī, ✓I is still helpful in finding some fresh new elements inĪ/I. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection
ideals, and generically Gorenstein ideals.
Part of the results contained in this paper were obtained while the first author was visiting Rutgers University and was partially
supported by CNR grant 203.01.63, Italy. The second and third authors were partially supported by the NSF.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag 相似文献
9.
Ahad Rahimi 《Journal of Pure and Applied Algebra》2007,211(1):83-93
In this paper we consider the local cohomology of monomial ideals with respect to monomial prime ideals and show that all these local cohomology modules are tame. 相似文献
10.
An idealI of the ringK[x
1, ...,x
n
] of polynomials over a fieldK inn indeterminates is a full ideal ifI is closed under substitution,f I,g
1...gn K[x
1, ...,x
n
] implyf(g
1, ...,g
n
) I. In this paper we continue the investigation of full ideals ofK[x
1, ...,x
n
]. In particular we determine several classes of full ideals ofK[x, y] (K a finite field) and investigate properties of these classes.The first author gratefully acknowledges support from theDeutsche Forschungsgemeinschaft 相似文献
11.
12.
Margherita Barile 《Archiv der Mathematik》2006,87(6):516-521
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms
of the number of its minimal monomial generators and the maximum height of its minimal primes.
Received: 12 December 2005 相似文献
13.
Jonathan A. Cox 《Journal of Pure and Applied Algebra》2008,212(1):1-8
This article introduces and advances the basic theory of “uniformly primary ideals” for commutative rings, a concept that imposes a certain boundedness condition on the usual notion of “primary ideal”. Characterizations of uniformly primary ideals are provided along with examples that give the theory independent value. Applications are also provided in contexts that are relevant to Noetherian rings. 相似文献
14.
Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to
describe it concretely once the generators of I are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing
for integral closedness, and in case , is still helpful in finding some fresh new elements in . Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection
ideals, and generically Gorenstein ideals.
Received: 28 July 1997 相似文献
15.
《Quaestiones Mathematicae》2013,36(6):717-732
AbstractLet R be a commutative ring. An ideal I of R is called a d-ideal (f d-ideal) provided that for each a ∈ I (finite subset F of I) and b ∈ R, Ann(a) ? Ann(b) (Ann(F) ? Ann(b)) implies that b ∈ I. It is shown that, the class of z0-ideals (hence all sz0-ideals), maximal ideals in an Artinian or in a Kasch ring, annihilator ideals, and minimal prime ideals over a d-ideal are some distinguished classes of d-ideals. Furthermore, we introduce the class of f d-ideals as a subclass of d-ideals in a commutative ring R. In this regard, it is proved that the ring R is a classical ring with property (A) if and only if every maximal ideal of R is an f d-ideal. The necessary and sufficient condition for which every prime f d-ideal of a ring R being a maximal or a minimal prime ideal is given. Moreover, the rings for which their prime d-ideals are z0-ideals are characterized. Finally, we prove that every prime f d-ideal of a ring R is a minimal prime ideal if and only if for each a ∈ R there exists a finitely generated ideal , for some n ∈ ? such that Ann(a, I) = 0. As a consequence, every prime f d-ideal in a reduced ring R is a minimal prime ideal if and only if X= Min(R) is a compact space. 相似文献
16.
Duong Quôc Viê.t 《Journal of Pure and Applied Algebra》2006,205(3):498-509
Let I be an equimultiple ideal of Noetherian local ring A. This paper gives some multiplicity formulas of the extended Rees algebras T=A[It,t-1]. In the case A generalized Cohen-Macaulay, we determine when T is Cohen-Macaulay and as an immediate consequence we obtain e.g., some criteria for the Cohen-Macaulayness of Rees algebra R(I) over a Cohen-Macaulay ring in terms of reduction numbers and ideals. 相似文献
17.
18.
Let R be a K-algebra acting densely on VD, where K is a commutative ring with unity and V is a right vector space over a division K-algebra D. Let ρ be a nonzero right ideal of R and let f(X1,…,Xt) be a nonzero polynomial over K with constant term 0 such that μR≠0 for some coefficient μ of f(X1,…,Xt). Suppose that d:R→R is a nonzero derivation. It is proved that if rankd(f(x1,…,xt))?m for all x1,…,xt∈ρ and for some positive integer m, then either ρ is generated by an idempotent of finite rank or d=ad(b) for some b∈End(VD) of finite rank. In addition, if f(X1,…,Xt) is multilinear, then b can be chosen such that rank(b)?2(6t+13)m+2. 相似文献
19.
J. Kališnik 《Indagationes Mathematicae》2008,19(1):73-96
Any étale Lie groupoid G is completely determined by its associated convolution algebra Cc∞(G) equipped with the natural Hopfalgebroid structure. We extend this result to the generalized morphisms between étale Lie groupoids: we show that any principal H-bundle P over G is uniquely determined by the associated Cc∞(G)-Cc∞(H)-bimodule Cc∞(P) equipped with the natural coalgebra structure. Furthermore, we prove that the functor Cc∞gives an equivalence between the Morita category of étale Lie groupoids and the Morita category of locally grouplike Hopf algebroids. 相似文献
20.
The purpose of this paper is twofold: first, to explain Gian-Carlo Rotas work
on invariant theory; second, to place this work in a broad historical and mathematical
context. Rotas work falls under three specific cases: vector invariants, the invariants of
binary forms, and the invariants of skew-symmetric tensors. We discuss each of these cases
and show how determinants and straightening play central roles. In fact, determinants
constitute all invariants in the vector case; for binary forms and skew-symmetric tensors,
they constitute all invariants when invariants are represented symbolically. Consequently,
we explain the symbolic method both for binary forms and for skew-symmetric tensors,
where Rota developed generalizations of the usual notion of a determinant. We also discuss
the Grassmann algebra, with its two operations of meet and join, which was a theme which
ran through Rotas work on invariant theory almost from the very beginning.To the memory of Gian-Carlo Rota 相似文献