共查询到20条相似文献,搜索用时 31 毫秒
1.
Given a homomorphism of commutative noetherian rings R→S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals , where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension. 相似文献
2.
?tefan O. Tohaˇneanu 《Journal of Pure and Applied Algebra》2011,215(11):2645-2651
Let K be a field of characteristic 0. Let be a reduced finite set of points, not all contained in a hyperplane. Let be the maximum number of points of Γ contained in any hyperplane, and let . If I⊂R=K[x0,…,xn] is the ideal of Γ, then in Tohaˇneanu (2009) [12] it is shown that for n=2,3, d(Γ) has a lower bound expressed in terms of some shift in the graded minimal free resolution of R/I. In these notes we show that this behavior holds true in general, for any n≥2: d(Γ)≥An, where An=min{ai−n} and ⊕iR(−ai) is the last module in the graded minimal free resolution of R/I. In the end we also prove that this bound is sharp for a whole class of examples due to Juan Migliore (2010) [10]. 相似文献
3.
Mohsen Asgharzadeh Kamran Divaani-Aazar Massoud Tousi 《Journal of Pure and Applied Algebra》2009,213(3):321-328
Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We explore the behavior of the two notions fa(M), the finiteness dimension of M with respect to a, and, its dual notion qa(M), the Artinianness dimension of M with respect to a. When (R,m) is local and r?fa(M) is less than , the m-finiteness dimension of M relative to a, we prove that is not Artinian, and so the filter depth of a on M does not exceed fa(M). Also, we show that if M has finite dimension and is Artinian for all i>t, where t is a given positive integer, then is Artinian. This immediately implies that if q?qa(M)>0, then is not finitely generated, and so fa(M)≤qa(M). 相似文献
4.
Sean Sather-Wagstaff 《Journal of Pure and Applied Algebra》2008,212(12):2594-2611
Let R be a local ring and M a finitely generated R-module. The complete intersection dimension of M-defined by Avramov, Gasharov and Peeva, and denoted -is a homological invariant whose finiteness implies that M is similar to a module over a complete intersection. It is related to the classical projective dimension and to Auslander and Bridger’s Gorenstein dimension by the inequalities .Using Blanco and Majadas’ version of complete intersection dimension for local ring homomorphisms, we prove the following generalization of a theorem of Avramov and Foxby: Given local ring homomorphisms φ:R→S and ψ:S→T such that φ has finite Gorenstein dimension, if ψ has finite complete intersection dimension, then the composition ψ°φ has finite Gorenstein dimension. This follows from our result stating that, if M has finite complete intersection dimension, then M is C-reflexive and is in the Auslander class AC(R) for each semidualizing R-complex C. 相似文献
5.
For a commutative noetherian ring R with residue field k stable cohomology modules have been defined for each n∈Z, but their meaning has remained elusive. It is proved that the k-rank of any characterizes important properties of R, such as being regular, complete intersection, or Gorenstein. These numerical characterizations are based on results concerning the structure of Z-graded k-algebra carried by stable cohomology. It is shown that in many cases it is determined by absolute cohomology through a canonical homomorphism of algebras . Some techniques developed in the paper are applicable to the study of stable cohomology functors over general associative rings. 相似文献
6.
Karim Samei 《Journal of Pure and Applied Algebra》2007,209(3):813-821
In this paper the zero-divisor graph Γ(R) of a commutative reduced ring R is studied. We associate the ring properties of R, the graph properties of Γ(R) and the topological properties of . Cycles in Γ(R) are investigated and an algebraic and a topological characterization is given for the graph Γ(R) to be triangulated or hypertriangulated. We show that the clique number of Γ(R), the cellularity of and the Goldie dimension of R coincide. We prove that when R has the annihilator condition and ; Γ(R) is complemented if and only if is compact. In a semiprimitive Gelfand ring, it turns out that the dominating number of Γ(R) is between the density and the weight of . We show that Γ(R) is not triangulated and the set of centers of Γ(R) is a dominating set if and only if the set of isolated points of is dense in . 相似文献
7.
C?t?lin Ciuperc? 《Journal of Pure and Applied Algebra》2003,178(1):25-48
Let A be a local ring with maximal ideal . For an arbitrary ideal I of A, we define the generalized Hilbert coefficients . When the ideal I is -primary, jk(I)=(0,…,0,(−1)kek(I)), where ek(I) is the classical kth Hilbert coefficient of I. Using these coefficients we give a numerical characterization of the homogeneous components of the S2-ification of S=A[It,t−1], extending previous results obtained by the author to not necessarily -primary ideals. 相似文献
8.
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
9.
10.
M. Jahangiri 《Journal of Pure and Applied Algebra》2009,213(4):573-581
Let R=?n≥0Rn be a homogeneous Noetherian ring, let M be a finitely generated graded R-module and let R+=?n>0Rn. Let b?b0+R+, where b0 is an ideal of R0. In this paper, we first study the finiteness and vanishing of the n-th graded component of the i-th local cohomology module of M with respect to b. Then, among other things, we show that the set becomes ultimately constant, as n→−∞, in the following cases:
- (i)
- and (R0,m0) is a local ring;
- (ii)
- dim(R0)≤1 and R0 is either a finite integral extension of a domain or essentially of finite type over a field;
- (iii)
- i≤gb(M), where gb(M) denotes the cohomological finite length dimension of M with respect to b.
11.
For a commutative ring R with zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we characterize when either or . We then use these results to investigate the diameter and girth for the zero-divisor graphs of polynomial rings, power series rings, and idealizations. 相似文献
12.
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
13.
D.P. Patil 《Journal of Pure and Applied Algebra》2006,205(2):266-278
In this article we characterize noetherian local one-dimensional analytically irreducible and residually rational domains (R,mR) which are non-Gorenstein, the non-negative integer is equal to τR-1 and ?(R/(C+xR))=2, where τR is the Cohen-Macaulay type of R, C is the conductor of R in the integral closure of R in its quotient field Q(R) and xR is a minimal reduction of m by giving some conditions on the numerical semi-group v(R) of R. 相似文献
14.
Jan O. Kleppe 《Journal of Pure and Applied Algebra》2011,215(7):1711-1725
A scheme X⊂Pn of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t×t minors of a homogeneous t×(t+c−1) matrix (fij). Given integers a0≤a1≤?≤at+c−2 and b1≤?≤bt, we denote by the stratum of standard determinantal schemes where fij are homogeneous polynomials of degrees aj−bi and is the Hilbert scheme (if n−c>0, resp. the postulation Hilbert scheme if n−c=0).Focusing mainly on zero and one dimensional determinantal schemes we determine the codimension of in and we show that is generically smooth along under certain conditions. For zero dimensional schemes (only) we find a counterexample to the conjectured value of appearing in Kleppe and Miró-Roig (2005) [25]. 相似文献
15.
16.
17.
Given two positive integers e and s we consider Gorenstein Artinian local rings R whose maximal ideal m satisfies ms≠0=ms+1 and rankR/m(m/m2)=e. We say that R is a compressed Gorenstein local ring when it has maximal length among such rings. It is known that generic Gorenstein Artinian algebras are compressed. If s≠3, we prove that the Poincaré series of all finitely generated modules over a compressed Gorenstein local ring are rational, sharing a common denominator. A formula for the denominator is given. When s is even this formula depends only on the integers e and s . Note that for s=3 examples of compressed Gorenstein local rings with transcendental Poincaré series exist, due to Bøgvad. 相似文献
18.
Let R be a commutative local noetherian ring, and let L and L′ be R-modules. We investigate the properties of the functors and . For instance, we show the following:
- (a)
- if L and L′ are artinian, then is artinian, and is noetherian over the completion ;
- (b)
- if L is artinian and L′ is Matlis reflexive, then , , and are Matlis reflexive.
19.