853 research outputs found
Updating Singular Value Decomposition for Rank One Matrix Perturbation
An efficient Singular Value Decomposition (SVD) algorithm is an important
tool for distributed and streaming computation in big data problems. It is
observed that update of singular vectors of a rank-1 perturbed matrix is
similar to a Cauchy matrix-vector product. With this observation, in this
paper, we present an efficient method for updating Singular Value Decomposition
of rank-1 perturbed matrix in time.
The method uses Fast Multipole Method (FMM) for updating singular vectors in
time, where is the
precision of computation
On the local cohomology modules deffined by a pair of ideals and serre subcategories
This paper is concerned about the relation between local cohomology modules
defined by a pair of ideals and Serre classes of R-modules, as a generalization
of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh
and M.Tousi (2010). Let R be a commutative Noetherian ring, I, J be two ideals
of R and M be an R-module. Let a\in \~{W}(I; J) and t \in N_0 be such that
Ext^t_R(R/a,M)\in S and Ext^j_R(R/a,H^i_I;J(M))\inS for all i =0.
Then for any submodule N of H^t_I;J(M) such that Ext^1_R(R/a;N)\in,we obtain
HomR(R=a;H^t_I;J(M)/N)\inS.Comment: 12 page
Faltings' local-global principle for the in dimension of local cohomology modules
The concept of Faltings' local-global principle for the in dimension of
local cohomology modules over a Noetherian ring is introduced, and it is
shown that this principle holds at levels 1, 2. We also establish the same
principle at all levels over an arbitrary Noetherian ring of dimension not
exceeding 3. These generalize the main results of Brodmann et al. in
\cite{BRS}. Moreover, as a generalization of Raghavan's result, we show that
the Faltings' local-global principle for the in dimension of local
cohomology modules holds at all levels whenever the ring
is a homomorphic image of a Noetherian Gorenstein ring. Finally, it is shown
that if is a finitely generated -module, an ideal of and
a non-negative integer such that is in
dimension for all and for some positive integer , then for any
minimax submodule of , the -module \Hom_R(R/\frak a,
H^r_{\frak a}(M)/N) is finitely generated. As a consequence, it follows that
the associated primes of are finite. This generalizes the
main results of Brodmann-Lashgari \cite{BL} and Quy \cite{Qu}.Comment: To appear in Communications in Algebra. arXiv admin note: substantial
text overlap with arXiv:1308.554
On the Attached prime ideals of local cohomology modules defined by a pair of ideals
Let and be two ideals of a commutative Noetherian ring and be
an -module of dimension . If is a complete local ring and is
finite, then attached prime ideals of are computed by means
of the concept of co-localization. Also, we illustrate the attached prime
ideals of on a non-local ring , for and .Comment: are welcome
On graded local cohomology modules defined by a pair of ideals
Let be a standard graded ring,
be a finite graded -module and be a homogenous ideal of . In this
paper we study the graded structure of the -th local cohomology module of
defined by a pair of ideals , i.e. . More
precisely, we discuss finiteness property and vanishing of the graded
components .
Also, we study the Artinian property and tameness of certain submodules and
quotient modules of .Comment: are welcome
On top local cohomology modules, Matlis duality and tensor products
Let be an ideal of a local ring with the cohomological dimension of in
. In the case that , we first give a bound for
depth~, where and is complete.
Later, ,
and
are examined. In the
case , the set Att is considered.Comment: 12 pages, This is the extended version of arXiv:1302.1274v1 and
arXiv:1212.0245. accepted to appear in Journal of Algebra and Its
Application
On the associated prime ideals of local cohomology modules defined by a pair of ideals
Let and be two ideals of a commutative Noetherian ring and be
an -module. For a non-negative integer it is shown that, if the sets
\Ass_R(\Ext^{n} _{R}(R/I,M)) and \Supp_R(\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))
are finite for all and all , then so is
\linebreak\Ass_R(\Hom_{R}(R/I,H^{n}_{I,J}(M))). We also study the finiteness
of \Ass_R(\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M))) for .Comment: are welcome
Some homological properties of ideals with cohomological dimension one
Let R denote a commutative Noetherian ring and let I be an ideal of R such
that H_i^I(R) = 0, for all integers i greater than or equal to 2. In this paper
we shall prove some results concerning the homological properties of I
Upper bounds, cofiniteness, and artinianness of local cohomology modules defined by a pair of ideals
Let be a commutative noetherian ring, be two ideals of , be
an -module, and be a Serre class of -modules. A positive
answer to the Hunekes conjecture is given for a noetherian ring and
minimax -module of krull dimension less than 3, with respect to
. There are some results on cofiniteness and artinianness of local
cohomology modules with respect to a pair of ideals. For a ZD-module of
finite krull dimension and an integer , if
\lc^{i}_{I,J}(M)\in\mathcal{S} for all , then
\lc^{i}_{I,J}(M)/\fa^{j}\lc^{i}_{I,J}(M)\in\mathcal{S} for any
\fa\in\tilde{W}(I,J), all , and all . By introducing the
concept of Seree cohomological dimension of with respect to , for an
integer , \lc^{j}_{I,J}(R)\in\mathcal{S} for all iff
\lc^{j}_{I,J}(M)\in\mathcal{S} for all and any finite -module .Comment: 13 page
Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules
Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite
R-module. It is shown that, if (R;m) is a complete local ring, then under
certain conditions a contains a regular element on DR(Hc a(M)), where c =
cd(a;M). A non-zerodivisor characterization of relative Cohen-Macaulay modules
w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered
modules w.r.t a and study some basic properties of such modules. In paticular,
we provide a non-zerodivisor characterization of relative Cohen-Macaulay
filtered modules w.r.t a. Furthermore, a characterization of cohomological
dimension filtration of M by the associated prime ideals of its factors is
established. As a consequence, we present a cohomological dimension filtration
for those modules whose zero submodule has a primary decomposition. Finally, we
bring some new results about relative Cohen- Macaulay modules w.r.t a.Comment: 15 page
- …