EUDML

Let $(R, 𝔪)$ be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated $R$ -module.

The amalgamated duplication of a ring along a semidualizing ideal

Maryam Salimi; Elham Tavasoli; Siamak Yassemi — 2013

Rendiconti del Seminario Matematico della Università di Padova

$k$ -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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G-Dimension.

Coassociated primes of modules over a commutative ring.

On the non-vanishing of local cohomology modules

The dual notion of prime submodules

Bounds on Bass numbers and their dual

The amalgamated duplication of a ring along a semidualizing ideal

$k$ -torsionless modules with finite Gorenstein dimension

Advanced Search

Formula preview

Currently displaying 1 – 7 of 7

G-Dimension.

Coassociated primes of modules over a commutative ring.

On the non-vanishing of local cohomology modules

The dual notion of prime submodules

Bounds on Bass numbers and their dual

The amalgamated duplication of a ring along a semidualizing ideal

k -torsionless modules with finite Gorenstein dimension

$k$ -torsionless modules with finite Gorenstein dimension