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This paper deals with the rings which satisfy $D C C_{d}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings and the...

Ringtopologien auf Z und Q.

Hans Weber (1977)

Mathematische Zeitschrift

Risoluzione di moduli su domini d'integrità noetheriani con proprietà di estensione

Santuzza Baldassarri Ghezzo (1972)

Rendiconti del Seminario Matematico della Università di Padova

Root closure in commutative rings

David F. Anderson, David E. Dobbs, Moshe Roitman (1990)

Annales scientifiques de l'Université de Clermont. Mathématiques

Root systems and hypergeometric functions. I

G. J. Heckman, E. M. Opdam (1987)

Compositio Mathematica

Root systems and hypergeometric functions. II

G. J. Heckman (1987)

Compositio Mathematica

Rückert Nullstellensatz for normed, non-discrete fields using non-standard analysis.

Păsărescu, Angela (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

$S$ -anneaux noethériens

Constantin Niţă (1975)

Rendiconti del Seminario Matematico della Università di Padova

$S$ -depth on $Z D$ -modules and local cohomology

Morteza Lotfi Parsa (2021)

Czechoslovak Mathematical Journal

Let $R$ be a Noetherian ring, and $I$ and $J$ be two ideals of $R$ . Let $S$ be a Serre subcategory of the category of $R$ -modules satisfying the condition $C_{I}$ and $M$ be a $Z D$ -module. As a generalization of the $S$ - $depth (I, M)$ and $depth (I, J, M)$ , the $S$ - $depth$ of $(I, J)$ on $M$ is defined as $S$ - $depth (I, J, M) = inf {S$ - $depth (𝔞, M) : 𝔞 \in \tilde{W} (I, J)}$ , and some properties of this concept are investigated. The relations between $S$ - $depth (I, J, M)$ and $H_{I, J}^{i} (M)$ are studied, and it is proved that $S$ - $depth (I, J, M) = inf {i : H_{I, J}^{i} (M) \notin S}$ , where $S$ is a Serre subcategory closed under taking injective hulls. Some conditions are provided that local cohomology modules with...

$S L_{2}$ , the cubic and the quartic

Yannis Y. Papageorgiou (1998)

Annales de l'institut Fourier

We describe the branching rule from $S p_{4}$ to $S L_{2}$ , where the latter is embedded via its action on binary cubic forms. We obtain both a numerical multiplicity formula, as well as a minimal system of generators for the geometric realization of the rule.

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