Results 61 to 70 of about 412,769 (93)

Cofinitely F-supplemented modules

São Paulo Journal of Mathematical Sciences, 2023
Let \(R\) be a unital ring, \(M\) a left \(R\)-module, and \(U,\, V\) and \(F\) submodules of \(M\) with \(F\) proper. \(V\) is an \(F\)-supplement of \(U\) in \(M\) if \(V\) is minimal in the collection of submodules \(F\subseteq X \subset M\) such that \(M = U + X\).
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Cofinitely generated and cofinitely related modules

Acta Mathematica Academiae Scientiarum Hungaricae, 1982
P. VAMOS [11] has defned and studied 'finitely embedded modules' as the dual of 'finitely generated modules'. JANS [4] called them as co finitely generated modules and defined a right co-noetherian ring as dual to a right noetherian ring and investigated their properties.
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Cofinitely projective modules II

Archiv der Mathematik, 1987
The author in an earlier paper [in J. Aust. Math. Soc., Ser. A 26, 330- 336 (1978; Zbl 0393.16018)], has studied finitely projective modules over a Dedekind domain and in Part I [Houston J. Math. 11, 183-190 (1985; Zbl 0576.16024)], he has studied cofinitely projective modules over a Dedekind domain. In this paper we study cofinitely projective modules
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Cofinitely g‐radical supplemented modules

Mathematical Methods in the Applied Sciences, 2020
In this work, all rings have unity and all modules are unital left modules. Let M be an R‐module. If every cofinite submodule of M has a g‐radical supplement in M, then M is called a cofinitely g‐radical supplemented module. In this work, some properties of cofinitely g‐radical supplemented modules are investigated.
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On Cofinitely Lifting and Cofinitely Weak Lifting Modules

Communications in Algebra, 2008
We say that a module M is lifting if M is amply supplemented and every supplement submodule of M is a direct summand. The module M is called cofinitely lifting if it is amply cofinitely supplemented and every supplement of any cofinite submodule of M is a direct summand. In this article various properties of cofinitely lifting modules are given.
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COFINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Bulletin of the Australian Mathematical Society, 2011
AbstractLet 𝔞 be an ideal of a Noetherian ring R. Let s be a nonnegative integer and let M and N be two R-modules such that ExtjR(M/𝔞M,Hi𝔞(N)) is finite for all i<s and all j≥0 . We show that HomR (R/𝔞,Hs𝔞(M,N)) is finite provided ExtsR(M/𝔞M,N) is a finite R-module.
Borna, Keivan, Sahandi, Parviz, Yassemi, Siamak   +2 more
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On cofinitely Rad-supplemented modules

2020
Let R be a ring and M be a left R-module. In this work some properties of (amply) cofinitely Rad-supplemented modules are developed. It is shown that if M contains a nonzero semi-hollow submodule then M is cofinitely Rad-supplemented if and only if M/N is cofinitely Rad-supplemented.
Türkmen E., Pancar A.
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Cofinitely Injective and Projective Modules

2020
In this work, cofinitely injective and cofinitely projective modules are defined. Some properties of cofinitely injective and cofinitely projective modules are investigated. Let N be an R-module. Then every R-module is cofinitely N-injective if and only if every cofinite submodule of N is a direct summand.
Nebiyev, C., Pancar, A.
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A recent generalization of cofinitely injective modules

2023
Summary: Let \(R\) be an associative ring with identity and \(M\) be a left \(R\)-module. In this paper, we define modules that have the property (\(\delta\)-\(CE\)) ((\(\delta\)-\(CEE\))), these are modules that have a \(\delta\)-supplement (ample \(\delta\)-supplements) in every cofinite extension which are generalized version of modules that have ...
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On the cofiniteness of local cohomology modules

2022
Summary: Let \(R\) be a commutative Noetherian ring with identity, \(I\) be an ideal of \(R\) and \(M\) be an \(R\)-module such that \(\mathrm{Ext}^j_R(R/I, M)\) is finitely generated for all \(j\). We prove that if \(\dim H^i_I(M)\leq 1\) for all \(i\), then for any \(i\geq 0\) and for any submodule \(N\) of \(H^i_I(M)\) that is either \(I\)-cofinite ...
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