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Cofinite modules and cofiniteness of local cohomology modules
Revista de la Unión Matemática ArgentinaAll rings in this review are commutative with identity and all modules are unitary. Let \(R\) be a Noetherian ring with non-zero identity, \(\mathfrak{a}\) an ideal of \(R,\) \(M\) a finitely generated (or finite for short) \(R\)-module, \(X\) an arbitrary \(R\)-module, and \(n\) a non-negative integer.
Vahidi, Alireza +2 more
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LINKAGE AND DUALITY OF MODULES [PDF]
, 2009 Martsinkovsky and Strooker [13] recently introduced module theoretic linkage using syzygy and transpose. This generalization brings possibility of much application of linkage, especially, to homological theory of modules. In the present paper, we connect
Nishida, Kenji, Kenji Nishida
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ON A GENERALIZATION OF COFINITELY LIFTING MODULES [PDF]
International Journal of Pure and Apllied Mathematics, 2014 In this paper, we study on cofinitely Rad-lifting modules as a proper generalization of modules with the property (P?) and cofinitely lifting modules, and we obtain the properties of these modules. In particular, we prove that if M with the property (SSP) is a cofinitely Rad-lifting module, then M/N is a cofinitely Rad-lifting module for every direct ...
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Cofiniteness of local cohomology modules and subcategories of modules [PDF]
, 2023 Let $R$ be a commutative noetherian ring and $I$ an ideal of $R$. Assume that for all integers $i$ the local cohomology module $H_I^i(R)$ is $I$-cofinite.
Takahashi, Ryo, Wakasugi, Naoki
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On cofinitely weak rad-supplemented modules
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2017 In this paper, necessary and sufficient conditions for a quotient module are found to be a cofinitely weak Rad-supplemented module under which circumstances. Nevertheless, some relations are investigated between cofinitely Rad-supplemented modules and cofinitely weak Rad-supplemented modules.
ERYILMAZ, Figen, EREN, Şenol
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On cofinitely weak $\delta-$ supplemented modules [PDF]
Miskolc Mathematical Notes, 2017 Let R be a ring and M be a left R-module. M is called cofinitely weak delta-supplemented ( or briefly delta-CWS-module) if every cofinite submodule of M has a weak delta-supplement in M. In this paper, we give various properties of this kind of modules.
ERYILMAZ, Figen, EREN, Şenol
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Endotrivial modules for the symmetric and alternating groups. [PDF]
, 2009 In this paper we determine the group of endotrivial modules for certain symmetric and alternating groups in characteristic $p$. If $p=2$, then the group is generated by the class of $\Omega^n(k)$ except in a few low degrees.
Mazza, Nadia +2 more
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Cohomological dimension, cofiniteness and Abelian categories of cofinite modules
Journal of Algebra, 2017 Let $R$ be a commutative Noetherian ring, $I$ be an ideal of $R$, and $M$ be an $R$-module. Recall that, the notion of the cohomological dimension of $M$ relative to $I$, denoted by $\mathrm{cd}(I,M)$, is defined to be the greatest integer $i$ such that $H_I^i(M)\neq 0$ if there exist such $i$'s and $-infty$ otherwise.
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A characterization result of cofinite local cohomology modules
, 2023 Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$, $M$ an arbitrary $R$-module and $N$ a finite $R$-module. We prove that \cite[Theorem 2.1]{Mel} and \cite[Proposition 3.3 (i)$\Leftrightarrow$(ii)]{B1} are true for any Serre subcategory of $
Melkersson, Leif, Aghapournahr, Moharram
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Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup. [PDF]
, 2013 Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2.
Mazza, Nadia +2 more
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