scholarly journals Change of grading, injective dimension and dualizing complexes

2018 ◽  
Vol 46 (10) ◽  
pp. 4414-4425 ◽  
Author(s):  
A. Solotar ◽  
P. Zadunaisky
Keyword(s):  
Injective Dimension ◽  
Dualizing Complexes

Dualizing complexes for commutative Noetherian rings

1975 ◽  
Vol 78 (3) ◽  
pp. 369-386 ◽  
Author(s):  
Rodney Y. Sharp
Keyword(s):  
Local Ring ◽  
Commutative Algebra ◽  
Present Author ◽  
Partial Solution ◽  
Noetherian Rings ◽  
Finitely Generated ◽  
Injective Dimension ◽  
Noetherian Local Ring ◽  
Dualizing Complexes

The theory of dualizing complexes of Grothendieck and Hartshorne ((5), chapter v) has turned out to be a useful tool even in commutative algebra. For instance, Peskine and Szpiro used dualizing complexes in their (partial) solution of Bass's conjecture concerning finitely-generated (f.-g.) modules of finite injective dimension over a Noetherian local ring ((7), chapitre I, §5); and the present author first obtained the results in (9) by using dualizing complexes.

Dualizing Complexes of Affine Semigroup Rings

1990 ◽  
Vol 322 (2) ◽  
pp. 561 ◽  
Author(s):  
Uwe Schafer ◽  
Peter Schenzel
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup ◽  
Dualizing Complexes

On Grothendieck's local duality theorem

1979 ◽  
Vol 85 (3) ◽  
pp. 431-437 ◽  
Author(s):  
M. H. Bijan-Zadeh ◽  
R. Y. Sharp
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Noetherian Ring ◽  
Duality Theorem ◽  
Great Emphasis ◽  
Triangulated Category ◽  
Elementary Approach ◽  
Commutative Noetherian Ring ◽  
Local Duality ◽  
Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

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].

Hopf algebras with rigid dualizing complexes

2008 ◽  
Vol 169 (1) ◽  
pp. 89-108 ◽  
Author(s):  
D.-M. Lu ◽  
Q.-S. Wu ◽  
J. J. Zhang
Keyword(s):  
Hopf Algebras ◽  
Dualizing Complexes
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