G-Dimension.
Coassociated primes of modules over a commutative ring.
On the non-vanishing of local cohomology modules
It is shown that for any Artinian modules , is the greatest integer such that .
The dual notion of prime submodules
In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.
Bounds on Bass numbers and their dual
Let be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated -module.
The amalgamated duplication of a ring along a semidualizing ideal
-torsionless modules with finite Gorenstein dimension
Let be a commutative Noetherian ring. It is shown that the finitely generated -module with finite Gorenstein dimension is reflexive if and only if is reflexive for with , and for with . 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 we give a characterization of -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...
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