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Anneaux de polynômes sur un anneau de Mori

Ballet, B., Dessagnes, N. (1988)

Portugaliae mathematica

Anneaux méta-noethériens

Paulo Ribenboim (1973/1974)

Séminaire Dubreil. Algèbre et théorie des nombres

Artinianness of formal local cohomology modules

Shahram Rezaei (2019)

Commentationes Mathematicae Universitatis Carolinae

Let $𝔞$ be an ideal of Noetherian local ring $(R, 𝔪)$ and $M$ a finitely generated $R$ -module of dimension $d$ . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to $𝔪$ . Also we prove that for an arbitrary local ring $(R, 𝔪)$ (not necessarily complete), we have ${Att}_{R} (𝔉_{𝔞}^{d} (M)) = Min V ({Ann}_{R} 𝔉_{𝔞}^{d} (M)) .$

Associated primes of local cohomology modules of generalized Laskerian modules

Dawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi (2019)

Czechoslovak Mathematical Journal

Let $ℐ$ be a set of ideals of a commutative Noetherian ring $R$ . We use the notion of $ℐ$ -closure operation which is a semiprime closure operation on submodules of modules to introduce the class of $ℐ$ -Laskerian modules. This enables us to investigate the set of associated prime ideals of certain $ℐ$ -closed submodules of local cohomology modules.

Bounding the Number of Generators of a Module.

Roger Wiegand, Wolmer Vasconcelos (1978/1979)

Mathematische Zeitschrift

Cardinality of generating sets for modules over a commutative ring.

Robert Gilmer, William Heinzer (1983)

Mathematica Scandinavica

Certain Complexes Associated to a Sequence and a Matrix.

Jürgen Herzog (1974)

Manuscripta mathematica

Des anneaux aux conditions des chaines ascendantes sur les idéaux de type n.

Anne-Marie Nicolas (1995)

Collectanea Mathematica

Equations for the set of overrings of normal rings and related ring extensions

Mabrouk Ben Nasr, Ali Jaballah (2023)

Czechoslovak Mathematical Journal

We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.

Essai d'une théorie noethérienne homogène pour les anneaux commutatifs dont la graduation est aussi générale que possible

Marcel Chadeyras (1970)

Mémoires de la Société Mathématique de France

Flat Ideals II.

W.V. Vasconcelos, Sarah Glaz (1977)

Manuscripta mathematica

Hilbert rings and the chain condition for prime ideals.

L.J. Ratliff (1976)

Journal für die reine und angewandte Mathematik

Injective Moduls over Krull Orders.

Robert Fossum (1971)

Mathematica Scandinavica

Intersections d'anneaux de Mori - exemples

Dessagnes, Nicole (1987)

Portugaliae mathematica

Loewy series of modules.

Thomas S. Shores (1974)

Journal für die reine und angewandte Mathematik

Matlis reflexive and generalized local cohomology modules

Amir Mafi (2009)

Czechoslovak Mathematical Journal

Let $(R, 𝔪)$ be a complete local ring, $𝔞$ an ideal of $R$ and $N$ and $L$ two Matlis reflexive $R$ -modules with $Supp (L) \subseteq V (𝔞)$ . We prove that if $M$ is a finitely generated $R$ -module, then ${Ext}_{R}^{i} (L, H_{𝔞}^{j} (M, N))$ is Matlis reflexive for all $i$ and $j$ in the following cases: (a) $\dim R / 𝔞 = 1$ ; (b) $cd (𝔞) = 1$ ; where $cd$ is the cohomological dimension of $𝔞$ in $R$ ; (c) $\dim R \leq 2$ . In these cases we also prove that the Bass numbers of $H_{𝔞}^{j} (M, N)$ are finite.

Multiplizitäten nichtnoetherscher Moduln über einem Ring.

Manfred Reufel (1976)

Journal für die reine und angewandte Mathematik

Noncoherence of a causal Wiener algebra used in control theory.

Sasane, Amol (2008)

Abstract and Applied Analysis

On commutative rings whose maximal ideals are idempotent

Farid Kourki, Rachid Tribak (2019)

Commentationes Mathematicae Universitatis Carolinae

We prove that for a commutative ring $R$ , every noetherian (artinian) $R$ -module is quasi-injective if and only if every noetherian (artinian) $R$ -module is quasi-projective if and only if the class of noetherian (artinian) $R$ -modules is socle-fine if and only if the class of noetherian (artinian) $R$ -modules is radical-fine if and only if every maximal ideal of $R$ is idempotent.

On h-regular graded algebras

Andrzej Tyc (1974)

Fundamenta Mathematicae

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