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Classifying subcategories of modules over a commutative noetherian ring

Classifying subcategories of modules over a commutative noetherian ring
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SUPERDECOMPOSABLE PURE INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS

Journal of Algebra and Its Applications, 2008
We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are "tame" according to the Klingler–Levy analysis in [4–6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.
PUNINSKAYA V., TOFFALORI, Carlo
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Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings

Georgian Mathematical Journal, 2008
Abstract We present the theory of Gröbner bases for the submodules of the free module 𝐴𝑚, 𝑚 ≥ 1, where 𝐴 = 𝑅[𝑥1,…,𝑥𝑛] and 𝑅 is a Noehterian commutative ring. This generalizes the theory of Gröbner bases for the ideals of 𝐴 and the submodules of (𝐾[𝑥1,…,𝑥𝑛])𝑚, where 𝐾 is a field, see [Möller, J. Symbolic Comput. 6: 345–359, 1988], [Möller,
Oswaldo Lezama
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Local Duality for Modules Over Noetherian Commutative Rings

Journal of Mathematical Sciences, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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UA-Properties of Modules Over Commutative Noetherian Rings

Russian Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D S Chistyakov, O V Lyubimtsev
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Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar)

Mathematische Annalen, 2007
Let \(A\) be a commutative noetherian ring. The support of a complex of \(A\)-modules is compared to the support of its cohomology. As a consequence the author classifies the full subcategories of \(A\)-modules that are thick (i.e. closed under taking kernels, cokernels and extensions) and closed under taking arbitrary direct sums.
Krause, Henning ; https://orcid.org/
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Artinian Serial Modules Over Commutative (or, Left Noetherian) Rings Are at Most One Step Away From Being Noetherian

Communications in Algebra, 2016
We introduce and study the concept of dual perfect dimension which is a Krull-like dimension extension of the concept of acc on finitely generated submodules. We observe some basic facts for modules with this dimension, which are similar to the basic properties of modules with Noetherian dimension.
O A S Karamzadeh
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Forcing Linearity Numbers of Semicyclic Modules Over Commutative Noetherian Rings

Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2003
Given a module \(V\) over a commutative ring \(R\), a function \(f:V\rightarrow V\) is said to be ``homogeneous'' if \(f(rv) = rf(v)\) for all \(r\in R\) and all \(v\in V\) and \(M_R(V)\) denotes the set of all such functions. Clearly \(M_R(V)\) is contained in \(\text{End}_R(V)\), the set of module endomorphisms on \(V\). This paper looks at how close
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Automorphism Groups of Noetherian Modules Over Commutative Rings

Archiv Der Mathematik, 1976
B A F Wehrfritz
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Gorenstein Dimension and Torsion of Modules Over Commutative Noetherian Rings

Communications in Algebra, 2000
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