Finite Modules of Finite Injective Dimension Over a Noetherian Algebra

2001 ◽  
Vol 63 (2) ◽  
pp. 319-335 ◽  
Author(s):  
Shiro Goto ◽  
Kenji Nishida
Keyword(s):  
Injective Dimension ◽  
Noetherian Algebra

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

A Bass Formula for Gorenstein Injective Dimension

2007 ◽  
Vol 35 (6) ◽  
pp. 1882-1889 ◽  
Author(s):  
Leila Khatami ◽  
Siamak Yassemi
Keyword(s):  
Injective Dimension ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

scholarly journals TRIVIAL MAXIMAL 1-ORTHOGONAL SUBCATEGORIES FOR AUSLANDER 1-GORENSTEIN ALGEBRAS

2013 ◽  
Vol 94 (1) ◽  
pp. 133-144
Author(s):  
ZHAOYONG HUANG ◽  
XIAOJIN ZHANG
Keyword(s):  
Projective Dimension ◽  
Indecomposable Module ◽  
Global Dimension ◽  
Injective Dimension ◽  
Tilted Algebra ◽  
Gorenstein Algebras

AbstractLet $\Lambda $ be an Auslander 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda $ admits a trivial maximal 1-orthogonal subcategory of $\text{mod } \Lambda $, then, for any indecomposable module $M\in \text{mod } \Lambda $, the projective dimension of $M$ is equal to one if and only if its injective dimension is also equal to one, and $M$ is injective if the projective dimension of $M$ is equal to two. In this case, we further get that $\Lambda $ is a tilted algebra.

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