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Let $R$ and $S$ be commutative rings with unity, $f : R \to S$ a ring homomorphism and $J$ an ideal of $S$ . Then the subring $R ⋈^{f} J : = {(a, f (a) + j) ∣ a \in R$ and $j \in J}$ of $R \times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$ . In this paper, we determine when $R ⋈^{f} J$ is a (generalized) filter ring.

Gröbner basis and depth of Rees algebras.

Popescu, Dorin (2001)

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

Homology of Local Flat Extensions and Complete Intersection Defects.

Luchezar L. Avramov (1977)

Mathematische Annalen

Ideals generated by minors of a symmetric matrix.

Tadeusz Józefiak (1978)

Commentarii mathematici Helvetici

Idéaux premiers de Goldman

Gabriel Picavet (1976)

Publications mathématiques et informatique de Rennes

Imbeddability of a commutative ring in a finite-dimensional ring.

Robert Gilmer, William Heinzer (1994)

Manuscripta mathematica

$k$ -torsionless modules with finite Gorenstein dimension

Maryam Salimi, Elham Tavasoli, Siamak Yassemi (2012)

Czechoslovak Mathematical Journal

Let $R$ be a commutative Noetherian ring. It is shown that the finitely generated $R$ -module $M$ with finite Gorenstein dimension is reflexive if and only if $M_{𝔭}$ is reflexive for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \leq 1$ , and ${G- dim}_{R_{𝔭}} (M_{𝔭}) \leq depth (R_{𝔭}) - 2$ for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \geq 2$ . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for $n \geq 2$ we give a characterization of $n$ -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...

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Efficient generation of zero dimensional ideals in polynomial rings.

Ein Cohen-Macaulay-Kriterium mit Anwendungen auf den Konormalenmodul und den Differentialmodul.

Eine Anwendung der Hasse-Schmidt-Differentiale auf ein Verzweigungsproblem.

Einige Eigenschaften der Parameterideale und ihre Anwendungen für Buchsbaum Ringe

El Espectro Y La Dimension De Anillos En El Algebra Sobre Un Topos.

Elementi indipendenti rispetto ad un ideale

Essential Sequences Over an Ideal and Essential Cograde.

Finite bases for integral closures.

Gabriel dimension of graded rings

(Generalized) filter properties of the amalgamated algebra

Gröbner basis and depth of Rees algebras.

Homology of Local Flat Extensions and Complete Intersection Defects.

Ideals generated by minors of a symmetric matrix.

Idéaux premiers de Goldman

Imbeddability of a commutative ring in a finite-dimensional ring.

$k$ -torsionless modules with finite Gorenstein dimension

Krull dimension and integrality of symmetric algebras.

Le spectre d'un anneau dans l'algèbre constructive et applications à la dimension

Length Formulas for the Local Cohomology of Exterior Powers.

Lengths of Submodule Chains Versus Krull Dimension in Non-Noetherian Modules.

Currently displaying 21 – 40 of 110