共查询到20条相似文献,搜索用时 15 毫秒
1.
Alan K. Kingsbury Rodney Y. Sharp 《Proceedings of the American Mathematical Society》1996,124(6):1703-1711
Let be ideals of the commutative ring , let be a Noetherian -module and let be a submodule of ; also let be an Artinian -module and let be a submodule of . It is shown that, whenever is a sequence of -tuples of non-negative integers which is non-decreasing in the sense that for all and all , then Ass is independent of for all large , and also Att is independent of for all large . These results are proved without any regularity conditions on the ideals , and so (a special case of) the first answers in the affirmative a question raised by S. McAdam.
2.
3.
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
4.
Let S be a polynomial ring and I be the Stanley-Reisner ideal of a simplicial complex Δ. The purpose of this paper is investigating the Buchsbaum property of S/I(r) when Δ is pure dimension 1. We shall characterize the Buchsbaumness of S/I(r) in terms of the graphical property of Δ. That is closely related to the characterization of the Cohen-Macaulayness of S/I(r) due to the first author and N.V. Trung. 相似文献
5.
Michael Hellus 《Archiv der Mathematik》2007,89(3):202-210
Let J be an ideal of a noetherian local ring R. We show new results on the set of attached primes
of a local cohomology module
. To prove our results we establish and use new relations between the set
of attached primes of a local cohomology module and the set
of associated primes of the Matlis dual of the same local cohomology module.
Received: 17 March 2006 相似文献
6.
Samir Bouchiba 《Journal of Pure and Applied Algebra》2007,209(3):621-630
This paper investigates the length of particular chains of prime ideals in tensor products of algebras over a field k. As an application, we compute dim(A⊗kA) for a new family of domains A that are k-algebras. 相似文献
7.
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
8.
We introduce a generalization of the notion of local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study its various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with ordinary local cohomology. 相似文献
9.
Fahimeh Khosh-Ahang 《Archiv der Mathematik》2008,90(1):18-23
In this paper, we compare Krull dimension, Gorenstein injective dimension and injective dimension of a module in several cases.
In fact, we establish some generalizations of the Bass formula. To this end, we generalize the Grothendieck non-vanishing
theorem to a class of modules larger than finitely generated modules.
Received: 21 May 2007 相似文献
10.
An ideal I of a ring R is said to be strongly irreducible if for ideals J and K of R, the inclusion J∩K⊆I implies that either J⊆I or K⊆I. The relationship among the families of irreducible ideals, strongly irreducible ideals, and prime ideals of a commutative ring R is considered, and a characterization is given of the Noetherian rings which contain a non-prime strongly irreducible ideal. 相似文献
11.
12.
Gunnar Fløystad 《Journal of Pure and Applied Algebra》2011,215(6):1255-1262
We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum theorem may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I. Barany and its generalizations by G. Kalai and R. Meshulam translate to the algebraic side. Our main results are algebraic generalizations of these translations, which in particular give a syzygetic version of Helly’s theorem. 相似文献
13.
《Quaestiones Mathematicae》2013,36(8):985-995
AbstractIn this paper we give some equivalent conditions for the C. Huneke’s two conjectures concerning the finiteness properties of the local cohomology module , where R is a regular local ring, I is an ideal of R and i ≥ 0 is an integer. 相似文献
14.
We study the regularity of binomial edge ideals. For a closed graph G we show that the regularity of the binomial edge ideal coincides with the regularity of and can be expressed in terms of the combinatorial data of G. In addition, we give positive answers to Matsuda‐Murai conjecture 8 for some classes of graphs. 相似文献
15.
Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley-Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley-Reisner and affine monoid algebras. We consider (non-pure) shellable fan’s and the Cohen-Macaulay property. Moreover, we study the local cohomology, the canonical module and the Gorenstein property of a toric face ring. 相似文献
16.
B. Banaschewski 《Order》1985,2(2):211-213
The prime ideal theorem for distributive lattices (PIT) is shown to imply that any complete distributive lattice with a compact unit has a prime element, which is then used to deduce from PIT that (1) every nontrivial ring with unit has a prime ideal, and (2) every Wallman locale is spatial. 相似文献
17.
Marco D’Anna Carmelo A. Finocchiaro Marco Fontana 《Journal of Pure and Applied Algebra》2010,214(9):1633-1641
Let f:A→B be a ring homomorphism and let J be an ideal of B. In this paper, we study the amalgamation of A with B along J with respect to f (denoted by A?fJ), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions (such as the A+XB[X], the A+XB?X? and the D+M constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension. 相似文献
18.
Taking the idea from classical Foxby equivalence, we develop an equivalence theory for derived categories over differential graded algebras. Both classical Foxby equivalence and the Morita equivalence for complete modules and torsion modules developed by Dwyer and Greenlees arise as special cases. 相似文献
19.
Shiv Datt Kumar 《Archiv der Mathematik》2007,89(2):124-130
Let A be a commutative Noetherian ring and
be an ideal containing a monic polynomial such that A[T]/I is zero dimensional. Suppose the conormal module I/I
2 is generated by r elements over A[T]/I. Then a set of r generators of
can be lifted to a r generating set of I.
A part of this work is done at the Abdus Salam, International Centre for Theoretical Physics, Trieste, Italy.
Received: 12 March 2006 Revised: 29 January 2007 相似文献
20.
We prove that multigraded Betti numbers of a simplicial forest are always either 0 or 1. Moreover a nonzero multidegree appears exactly in one homological degree in the resolution. Our work generalizes work of Bouchat [2] on edge ideals of graph trees. 相似文献