Results 101 to 110 of about 185 (137)

Generalized formal local cohomology modules

2023
Let \(\mathfrak{a}\) denote an ideal of a local Noetherian ring \((R,\mathfrak{m}). \) Let \(M,N\) be two \(R\)-modules. A. Grothendieck (see [\textit{A. Grothendieck}, Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne.
Rezaei, Shahram, Lashkari, Fatemeh
openaire   +2 more sources

Top Local Cohomology Modules

Algebra Colloquium, 2007
For a finitely generated module M over a commutative Noetherian local ring (R,𝔪), it is shown that there exist only a finite number of non-isomorphic top local cohomology modules [Formula: see text] for all ideals 𝔞 of R. It is also shown that for a given integer r ≥ 0, if [Formula: see text] is zero for all 𝔭 in Supp (M), then [Formula: see text] for
Dibaei, Mohammad T., Yassemi, Siamak
openaire   +2 more sources

Cohomological Dimension of Generalized Local Cohomology Modules

Algebra Colloquium, 2008
The study of the cohomological dimension of algebraic varieties has produced some interesting results and problems in local algebra. Let 𝔞 be an ideal of a commutative Noetherian ring R. For finitely generated R-modules M and N, the concept of cohomological dimension cd 𝔞(M, N) of M and N with respect to 𝔞 is introduced.
Amjadi, Jafar, Naghipour, Reza
openaire   +1 more source

Cofiniteness of Local Cohomology Modules

Algebra Colloquium, 2014
Let M be a non-zero finitely generated module over a commutative Noetherian local ring (R, 𝔪). In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t ≥ 0 is an integer and [Formula: see text], then [Formula: see text] is not 𝔭-cofinite.
Bahmanpour, Kamal, Naghipour, Reza, Sedghi, Monireh   +2 more
openaire   +2 more sources

de Rham cohomology of local cohomology modules II

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2018
Let $K$ be an algebraically closed field of characteristic zero, $R = K[x_1, \dots, x_n]$, $I$ be an ideal in $R$ and $A_n(K) = K \langle x_1, \dots, x_n, \partial_1, \dots, \partial_n\rangle$ be the $n$th Weyl algebra over $K$. For a given holonomic left $A_n(K)$-module $N$, let $\partial=\partial_1, \dots, \partial_n$ be pairwise commuting $K$-linear
Puthenpurakal, Tony J., Reddy, Rakesh B. T.   +1 more
openaire   +1 more source

Artinian Local Cohomology Modules

Canadian Mathematical Bulletin, 2007
AbstractLet R be a commutative Noetherian ring, α an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module is finitely generated for all i < t, then is finitely generated.
Keivan Borna Lorestani, Parviz Sahandi, Siamak Yassemi   +2 more
openaire   +1 more source

Artinian local cohomology modules of cofinie modules

Journal of Algebra and Its Applications, 2020
Let [Formula: see text] be a commutative Noetherian complete local ring and [Formula: see text] be a proper ideal of [Formula: see text]. Suppose that [Formula: see text] is a nonzero [Formula: see text]-cofinite [Formula: see text]-module of Krull dimension [Formula: see text].
openaire   +1 more source

Noetherianness and Local Cohomology Modules

Algebra Colloquium, 2012
Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M an R-module. We show that, whenever [Formula: see text], M is Noetherian if and only if there exists a submodule N of M such that the R-modules M/𝔞 N and [Formula: see text] are Noetherian.
openaire   +1 more source

Matlis dual of local cohomology modules

Czechoslovak Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naal, Batoul, Khashyarmanesh, Kazem
openaire   +1 more source