Results 81 to 90 of about 111 (101)
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Local Duality for Modules over Noetherian Commutative Rings
Journal of Mathematical Sciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On $$\jmath $$-Noetherian Modules over Commutative Rings
Iranian Journal of ScienceThe purpose of this study is to characterize modules V and submodules j where every submodule N of V not contained in j is finitely generated. Modules satisfying this condition are called j-Noetherian modules.
Erdemir, Dilara +3 more
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INTEGRAL CLOSURES OF IDEALS RELATIVE TO INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS
The Quarterly Journal of Mathematics, 1991In this article, motivated by the work of Northcott-Rees, Brodmann and Ratliff concerning the asymptotic behaviour (of integral closures) of powers of a fixed ideal of a Noetherian ring, the authors show the following: Let \({\mathfrak a}\) denote an ideal of a Noetherian ring \(A\) and \(E\) an injective \(A\)-module.
Toroghy, H. Ansari, Sharp, R. Y.
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Nonnil-Noetherian modules over commutative rings
2015Summary: In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let \(R\) be a commutative ring with identity and let \(M\) be an \(R\)-module such that \(\mathrm{Nil}(M)\) is a divided prime submodule of \(M\). \(M\) is called a nonnil-Noetherian \(R\)-module if every nonnil submodule of \(M\) is
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Krull Dimension of Injective Modules Over Commutative Noetherian Rings
Canadian Mathematical Bulletin, 2005AbstractLet R be a commutative Noetherian integral domain with field of fractions Q. Generalizing a forty-year-old theorem of E. Matlis, we prove that the R-module Q/R (or Q) has Krull dimension if and only if R is semilocal and one-dimensional. Moreover, if X is an injective module over a commutative Noetherian ring such that X has Krull dimension ...
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COMMUTATIVE RINGS AND MODULES THAT ARE r-NOETHERIAN
2022In this paper, we introduce and investigate a new class of modules that is closely related to the class of Noetherian modules. Let R be a commutative ring and M be an R-module. We say that M is an r-Noetherian module if every r-submodule of M is finitely generated. Also, we call the ring R to be an r-Noetherian ring if R is an r-Noetherian R-module, or
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Some Properties of Commutative Noetherian Rings and Modules
The investigation of Noetherian rings has drawn the attention of many scientists. In a recent investigation, Kosan and Quynh explored novel properties of Noetherian rings, especially as they relate to the fundamental extended and the direct sum of the injecting shells of basic right modules.Raghad I.zidan, Rouaa S. Μohammed
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Southeast Asian Bulletin of Mathematics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Tame-Wild Dichotomy for Commutative Noetherian Rings—A Survey
Springer Proceedings in Mathematics and Statistics, 2022Lee Klingler +2 more
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