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Cofiniteness of torsion functors of a pair of cofinite modules
Communications in Algebra, 2021Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules Tor i R ( N , M ) are I-cofinite for all i ≥ 0 if M and N are I-cofinite R-modules and N is of dimension at most...
Kamal Bahmanpour
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On Modules Having Small Cofinite Irreducibles
Canadian Mathematical Bulletin, 1994 AbstractIn this paper we obtain several new characterizations of modules having small cofinite irreducibles. One of these characterizations involves a metric topology defined on the submodule lattice.
Johnson, E. W. +2 more
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Communications in Algebra, 2016
Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is shown that the R-module is finitely generated, for all i ≥ 0, if and only if the R-module is finitely generated, for all 0 ≤ i ≤ ara(I). As an immediate consequence, we prove that, if R is a Noetherian (resp.
Kamal Bahmanpour +1 more
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Let R be a commutative Noetherian ring, I an ideal of R, and M an arbitrary R-module. It is shown that the R-module is finitely generated, for all i ≥ 0, if and only if the R-module is finitely generated, for all 0 ≤ i ≤ ara(I). As an immediate consequence, we prove that, if R is a Noetherian (resp.
Kamal Bahmanpour +1 more
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On a category of cofinite modules which is Abelian
Mathematische Zeitschrift, 2010Let \(I\) be an ideal of a commutative noetherian local ring \((R,\mathfrak{m})\) and \(M\) a finitely generated \(R\)-module. In 1968, \textit{A. Grothendieck} [Séminaire de géométrie algébrique: Cohomologie locale des faisceaux cohérents et théoremes de Lefschetz locaux et globaux (1962; Zbl 0159.50402)] has conjectured that \(\Hom_R(R/I,H_{I}^i(M))\)
Ken-Ichiroh Kawasaki
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Cofinite modules and local cohomology [PDF]
Journal of Pure and Applied Algebra, 1997 We show that if M is a finitely generated module over a commutative Noetherian local ring R and I is a dimension one ideal of R (i.e., dimRI = 1), then the local cohomology modules HIi(M) are I-cofinite; that is, ExtRj(RI, HIi(M)) is finitely generated ...
Donatella Delfino +3 more
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Cofinitely semiperfect modules
Siberian Mathematical Journal, 2005Summary: It is well known that a projective module \(M\) is \(\oplus\)-supplemented if and only if \(M\) is semiperfect. We show that a projective module \(M\) is \(\oplus\)-cofinitely supplemented if and only if \(M\) is cofinitely semiperfect or briefly cof-semiperfect (i.e., each finitely generated factor module of \(M\) has a projective cover).
Çalışıcı, Hamza, Pancar, Ali
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Algebra Colloquium, 2010
Let R be a ring and M a right R-module. M is called a cofinitely lifting module if for any cofinite submodule N of M, there exists a direct summand K of M such that K ≤ N and N/K ≪ M/K. It is proved that every cofinite direct summand of a cofinitely lifting module is cofinitely lifting. For a cofinitely lifting module M and a fully invariant submodule
Wang, Yongduo, Wu, Dejun
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Let R be a ring and M a right R-module. M is called a cofinitely lifting module if for any cofinite submodule N of M, there exists a direct summand K of M such that K ≤ N and N/K ≪ M/K. It is proved that every cofinite direct summand of a cofinitely lifting module is cofinitely lifting. For a cofinitely lifting module M and a fully invariant submodule
Wang, Yongduo, Wu, Dejun
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Cofiniteness of Local Cohomology Modules
Algebra Colloquium, 2014Let 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 +2 more
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On the Abelian categories of cofinite modules
Journal of Algebra and Its Applications, 2022Let [Formula: see text] be a commutative Noetherian ring and [Formula: see text] be an ideal of [Formula: see text] such that the [Formula: see text]-modules [Formula: see text] are [Formula: see text]-cofinite, for all finitely generated [Formula: see text]-modules [Formula: see text] and all [Formula: see text].
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