共查询到20条相似文献,搜索用时 31 毫秒
1.
Let R be a complete semi-local ring with respect to the topology defined by its Jacobson radical, a an ideal of R, and M a finitely generated R-module. Let D
R
(−) := Hom
R
(−, E), where E is the injective hull of the direct sum of all simple R-modules. If n is a positive integer such that Ext
R
j
(R/a, D
R
(H
a
t
(M))) is finitely generated for all t > n and all j ⩾ 0, then we show that Hom
R
(R/a, D
R
(H
a
n
(M))) is also finitely generated. Specially, the set of prime ideals in Coass
R
(H
a
n
(M)) which contains a is finite.
Next, assume that (R, m) is a complete local ring. We study the finiteness properties of D
R
(H
a
r
(R)) where r is the least integer i such that H
a
r
(R) is not Artinian. 相似文献
2.
In this note we give a simple proof of the following result: Let R be a commutative Noetherian ring, an ideal of R and M a finite R-module, if H i (M) has finite support for all i < n, then Ass(H n (M)) is finite. 相似文献
3.
Let X be a complex analytic manifold. Consider S?M?Xreal analytic submonifolds with codium R MS=1,and let ω be a connected component of M\S. Let p∈S XMTM *X where T* Xdenotes the conormal bundle to M in X, and denote by ν(p) the complex radial Euler field at p. Denote by μ*(Ox) (for * = M, ω) the microlocalization of the sheaf of holomorphic functions along *. Under the assumption dimR(TpTM *X? ν(p)) = 1, a theorem of vanishing for the cohomology groups HjμM(Ox)p is proved in [K-S 1, Prop. 11.3.1], j being related to the number of positive and negative eigenvalue for the Levi form of M. Under the hypothesis dimR(TpTS *X∩ν(p))=1, a similar result is proved here for the cohomology groups of the complex of microfunctions at the boundary μω(Ox).Stating this result in terms of regularity at the boundary for CR–hyperfunctions a local Bochner–type theorem is then obtained. 相似文献
4.
Reza Sazeedeh 《Proceedings Mathematical Sciences》2007,117(4):429-441
Let M be a finitely generated graded module over a Noetherian homogeneous ring R with local base ring (R
0, m0). If R
0 is of dimension one, then we show that reg
i+1(M) and coreg
i+1(M) are bounded for all i ∈ ℕ0. We improve these bounds, if in addition, R
0 is either regular or analytically irreducible of unequal characteristic. 相似文献
5.
Amir Mafi 《Proceedings Mathematical Sciences》2009,119(2):159-164
Let a be an ideal of a commutative Noetherian ring R with non-zero identity and let N be a weakly Laskerian R-module and M be a finitely generated R-module. Let t be a non-negative integer. It is shown that if H
a
i
(N) is a weakly Laskerian R-module for all i < t, then Hom
R
(R/a, H
a
t
(M, N)) is weakly Laskerian R-module. Also, we prove that Ext
R
i
(R/a, H
a
t
)) is weakly Laskerian R-module for all i = 0, 1. In particular, if Supp
R
(H
a
i
(N)) is a finite set for all i < t, then Ext
R
i
(R/a, H
a
t
(N)) is weakly Laskerian R-module for all i = 0, 1. 相似文献
6.
7.
8.
Jonathan Shick 《代数通讯》2013,41(4):1371-1388
The local cohomology modules HJ I(M) of a Matlis reflexive module are shown to be I-cofinite when j >= 1 and have finite Bass numbers when j >= 0, where I is an ideal satisfying any one of a list of properties. In addition, we show that the completion of a Matlis reflexive module is finitely generated over the completion of the ring and we classify Matlis reflexive modules over a one dimensional ring. 相似文献
9.
10.
Let R be a local ring and let (x
1, …, x
r) be part of a system of parameters of a finitely generated R-module M, where r < dimR
M. We will show that if (y
1, …, y
r) is part of a reducing system of parameters of M with (y
1, …, y
r) M = (x
1, …, x
r) M then (x
1, …, x
r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V
R(x
1, …, x
r) with dimR
R/P = dimR
M − r the localization M
P of M at P is an r-dimensional Cohen-Macaulay module over R
P.
Furthermore, we will show that M is a Cohen-Macaulay module iff y
d is a non zero divisor on M/(y
1, …, y
d−1) M, where (y
1, …, y
d) is a reducing system of parameters of M (d:= dimR
M). 相似文献
11.
Amir Mafi 《数学学报(英文版)》2009,25(6):917-922
Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module Ha^d(M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions. 相似文献
12.
Thomas Marley 《manuscripta mathematica》2001,104(4):519-525
Let R be a commutative Noetherian local ring of dimension d, I an ideal of R, and M a finitely generated R-module. We prove that the set of associated primes of the local cohomology module H
i
I
(M) is finite for all i≥ 0 in the following cases: (1) d≤ 3; (2) d= 4 and $R$ is regular on the punctured spectrum; (3) d= 5, R is an unramified regular local ring, and M is torsion-free. In addition, if $d>0$ then H
d
− 1
I
(M) has finite support for arbitrary R, I, and M.
Received: 31 October 2000 / Revised version: 8 January 2001 相似文献
13.
Peter Schenzel 《Archiv der Mathematik》2010,95(2):115-123
Let ${(R, \mathfrak{m})}Let
(R, \mathfrakm){(R, \mathfrak{m})} denote a local ring. Let I ì R{I \subset R} be an ideal with c = grade I. Let D(·) denote the Matlis duality functor. In recent research there is an interest in the structure of the local cohomology module
HcI : = HcI(R){H^c_I := H^c_I(R)}, in particular in the endomorphism ring of D(HcI){D(H^c_I)}. Let E
R
(k) be the injective hull of the residue field
R/\mathfrakm{R/\mathfrak{m}}. By investigating the natural map HcI ?D(HcI) ? ER(k){H^c_I \otimes D(H^c_I) \to E_R(k)} we are able to prove that the endomorphism rings of D(HcI){D(H^c_I)} and of HcI{H^c_I} are naturally isomorphic. This natural homomorphism is related to a quasi-isomorphism of a certain complex. As applications
we show results when the endomorphism ring of D(HcI){D(H^c_I)} is naturally isomorphic to R generalizing results known under the additional assumption of HiI(R) = 0{H^i_I(R) = 0} for i 1 c{i \not= c}. 相似文献
14.
Ahmad Abbasi Hajar Roshan-Shekalgourabi Dawood Hassanzadeh-Lelekaami 《Czechoslovak Mathematical Journal》2014,64(2):327-333
Let R be a commutative Noetherian ring with identity and I an ideal of R. It is shown that, if M is a non-zero minimax R-module such that dim Supp H I i (M) ? 1 for all i, then the R-module H I i (M) is I-cominimax for all i. In fact, H I i (M) is I-cofinite for all i ? 1. Also, we prove that for a weakly Laskerian R-module M, if R is local and t is a non-negative integer such that dim Supp H I i (M) ? 2 for all i < t, then Ext R j (R/I,H I i (M)) and Hom R (R/I,H I t (M)) are weakly Laskerian for all i < t and all j ? 0. As a consequence, the set of associated primes of H I i (M) is finite for all i ? 0, whenever dim R/I ? 2 and M is weakly Laskerian. 相似文献
15.
Amir Mafi 《Czechoslovak Mathematical Journal》2009,59(4):1095-1102
Let (R,m) be a complete local ring, a an ideal of R and N and L two Matlis reflexive R-modules with Supp(L) ⊆ V(a). We prove that if M is a finitely generated R-module, then Exti
R
i
(L, H
a
j
(M,N)) is Matlis reflexive for all i and j in the following cases:
In these cases we also prove that the Bass numbers of H
a
j
(M, N) are finite. 相似文献
(a) | dim R/a = 1 |
(b) | cd(a) = 1; where cd is the cohomological dimension of a in R |
(c) | dim R ⩽ 2. |
16.
For a commutative ring R with identity, an ideal-based zero-divisor graph, denoted by Γ I (R), is the graph whose vertices are {x ∈ R?I | xy ∈ I for some y ∈ R?I}, and two distinct vertices x and y are adjacent if and only if xy ∈ I. In this article, we investigate an annihilator ideal-based zero-divisor graph by replacing the ideal I with the annihilator ideal Ann(M) for a multiplication R-module M. Based on the above-mentioned definition, we examine some properties of an R-module over a von Neumann regular ring, and the cardinality of an R-module associated with Γ Ann(M)(R). 相似文献
17.
《代数通讯》2013,41(6):2553-2573
The first note shows that the integral closure L′ of certain localities L over a local domain R are unmixed and analytically unramified, even when it is not assumed that R has these properties. The second note considers a separably generated extension domain B of a regular domain A, and a sufficient condition is given for a prime ideal p in A to be unramified with respect to B (that is, p B is an intersection of prime ideals and B/P is separably generated over A/p for all P ∈ Ass (B/p B)). Then, assuming that p satisfies this condition, a sufficient condition is given in order that all but finitely many q ∈ S = {q ∈ Spec(A), p ? q and height(q/p) = 1} are unramified with respect to B, and a form of the converse is also considered. The third note shows that if R′ is the integral closure of a semi-local domain R, then I(R) = ∩{R′ p′ ;p′ ∈ Spec(R′) and altitude(R′/p′) = altitude(R′) ? 1} is a quasi-semi-local Krull domain such that: (a) height(N *) = altitude(R) for each maximal ideal N * in I(R); and, (b) I(R) is an H-domain (that is, altitude(I(R)/p *) = altitude(I(R)) ? 1 for all height one p * ∈ Spec(I(R))). Also, K = ∩{R p ; p ∈ Spec(R) and altitude(R/p) = altitude(R) ? 1} is a quasi-semi-local H-domain such that height (N) = altitude(R) for all maximal ideals N in K. 相似文献
18.
19.
20.
M. Brodmann 《Archiv der Mathematik》2002,79(2):87-92
Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ \infty and let \mathfrak a \subseteqq R {\mathfrak a} \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) = \textrm{Ass}_R(H_{\mathfrak a}^d (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) H_{\mathfrak a}^d (M) in terms of the local formal behaviour of \mathfrak a {\mathfrak a} . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) \textrm{Supp}_R(H_{\mathfrak a}^d (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢? X \nu : X' \rightarrow X contains points which are isolated in n-1(Spec(R/\mathfrak a)) \nu^{-1}(\textrm{Spec}(R/{\mathfrak a})) . 相似文献