On injective and Gorenstein injective dimensions of local cohomology modules
Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …
Generalized local cohomology modules and homological Gorenstein dimensions
K Divaani-Aazar, A Hajikarimi - Communications in Algebra®, 2011 - Taylor & Francis
Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …
Special homological dimensions and intersection theorem
T Sharif, S Yassemi - Mathematica Scandinavica, 2005 - JSTOR
Let (R, m) be commutative Noetherian local ring. It is shown that R is Cohen-Macaulay ring if
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …
there exists a Cohen-Macaulay finite (ie finitely generated) R-module with finite upper …
Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module
Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …
A generalization of a theorem of Bass
S Yassemi - Communications in Algebra, 2006 - Taylor & Francis
Let (R, 𝔪) be a commutative Noetherian local ring. In this paper we prove that if R admits a
finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is …
finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is …
On restricted injective dimensions of complexes
W Dejun, L Zhongkui - Communications in Algebra, 2013 - Taylor & Francis
Let R be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …
Modules with finite reducing Gorenstein dimension
T Araya, O Celikbas, J Cook, T Kobayashi - Beiträge zur Algebra und …, 2024 - Springer
If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …
Homological dimensions of rigid modules
We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …
homological dimensions of certain finitely generated modules. Our argument has a series of …
The existence of finitely generated modules of finite Gorenstein injective dimension
R Takahashi - Proceedings of the American Mathematical Society, 2006 - JSTOR
The Existence of Finitely Generated Modules of Finite Gorenstein Injective Dimension Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 134, Number 11 …
Gorenstein injective modules and local cohomology
R Sazeedeh - Proceedings of the American Mathematical Society, 2004 - ams.org
In this paper we assume that $ R $ is a Gorenstein Noetherian ring. We show that if
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …