When does the canonical module of a module have finite injective dimension?

2021 ◽  
Author(s):  
T. H. Freitas ◽  
V. H. Jorge Pérez
Keyword(s):  
Injective Dimension ◽  
Canonical Module

On Duality Relative to Self-orthogonal Bimodules

2005 ◽  
Vol 12 (02) ◽  
pp. 319-332
Author(s):  
Jun Wu ◽  
Wenting Tong
Keyword(s):  
Noetherian Ring ◽  
Injective Dimension ◽  
Left And Right

Let R be a left and right Noetherian ring and RωR a faithfully balanced self-orthogonal bimodule. We introduce the notions of special embeddings and modules of ω-D-class n, and then give some characterizations of them. As an application, we study the properties of RωR with finite injective dimension. Our results extend the main results in [4].

WEAK AB-CONTEXT FOR FP-INJECTIVE MODULES WITH RESPECT TO SEMIDUALIZING MODULES

2013 ◽  
Vol 12 (07) ◽  
pp. 1350039 ◽  
Author(s):  
JIANGSHENG HU ◽  
DONGDONG ZHANG
Keyword(s):  
Noetherian Ring ◽  
Model Structure ◽  
Injective Dimension ◽  
Commutative Noetherian Ring ◽  
New Model ◽  
Injective Modules ◽  
Semidualizing Modules ◽  
Semidualizing Bimodule ◽  
Gorenstein Injective

Let S and R be rings and SCR a semidualizing bimodule. We define and study GC-FP-injective R-modules, and these modules are exactly C-Gorenstein injective R-modules defined by Holm and Jørgensen provided that S = R is a commutative Noetherian ring. We mainly prove that the category of GC-FP-injective R-modules is a part of a weak AB-context, which is dual of weak AB-context in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander–Buchweitz approximations for R-modules with finite GC-FP-injective dimension. As an application, a new model structure in Mod R is given.

scholarly journals Ideals of injective dimension $1$.

1982 ◽  
Vol 29 (3) ◽  
pp. 335-356 ◽  
Author(s):  
Eben Matlis
Keyword(s):  
Injective Dimension
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