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On the formal grade of finitely generated modules over local rings
Mohsen Asgharzadeh, Kamran Divaani-Aazar
Let \fa be an ideal of a local ring (R,\fm) and M a finitely generated R-module. This paper concerns the notion \fgrade(\fa,M), the formal grade of M with respect to \fa (i.e. the…
Finiteness properties of formal local cohomology modules and Cohen-Macaulayness
Mohsen Asgharzadeh, Kamran Divaani-Aazar
Let $\fa$ be an ideal of a local ring $(R,\fm)$ and a finitely generated -module. We investigate the structure of the formal local cohomology modules ${\vpl}_nH^i_{\fm}(M/\f…
The finiteness dimension of local cohomology modules and its dual notion
Mohsen Asgharzadeh, Kamran Divaani-Aazar, Massoud Tousi
Let \fa be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We explore the behavior of the two notions f_{\fa}(M), the finiteness dimension of M wit…
Generalized local cohomology modules and homological Gorenstein dimensions
Kamran Divaani-Aazar, Alireza Hajikarimi
Let \fa be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let \cd_{\fa}(M,N) denote the supremum of the i's such that H^i_{\fa}(M,N)\neq…