scholarly journals On flat generators and Matlis duality for quasicoherent sheaves

2020 ◽  
Author(s):  
Alexander Slávik ◽  
Jan Šťovíček
Keyword(s):  
Matlis Duality

Matlis duality

2012 ◽  
pp. 193-210
Author(s):  
M. P. Brodmann ◽  
R. Y. Sharp
Keyword(s):  
Matlis Duality

GENERALIZED MATLIS DUALITY AND LINEAR COMPACTNESS

2002 ◽  
Vol 30 (4) ◽  
pp. 2075-2084 ◽  
Author(s):  
Weimin Xue
Keyword(s):  
Matlis Duality

GRADED MATLIS DUALITY AND APPLICATIONS TO COVERS

2001 ◽  
Vol 24 (4) ◽  
pp. 555-564 ◽  
Author(s):  
Edgar E. Enochs ◽  
J. A. López-Ramos
Keyword(s):  
Matlis Duality

On Sequentially Co-Cohen–Macaulay Modules

2007 ◽  
Vol 14 (03) ◽  
pp. 455-468
Author(s):  
Nguyen Thi Dung
Keyword(s):  
Artinian Modules ◽  
Local Homology ◽  
Matlis Duality ◽  
Artinian Module

In this paper, we define the notion of dimension filtration of an Artinian module and study a class of Artinian modules, called sequentially co-Cohen–Macaulay modules, which contains strictly all co-Cohen–Macaulay modules. Some characterizations of co-Cohen–Macaulayness in terms of the Matlis duality and of local homology are also given.

Artinian modules over commutative rings

1992 ◽  
Vol 111 (1) ◽  
pp. 25-33 ◽  
Author(s):  
R. Y. Sharp
Keyword(s):  
Commutative Ring ◽  
Local Ring ◽  
Commutative Rings ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Artinian Modules ◽  
Noetherian Local Ring ◽  
Matlis Duality ◽  
Artinian Module

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring R (throughout the paper, R will denote a commutative ring with identity) can, for some purposes at least, be reduced to the study of an Artinian module A' over a complete (Noetherian) local ring; in the latter situation, Matlis' duality 1 (alternatively, see 6, ch. 5) is available, and this means that the investigation can often be converted into a dual one about a finitely generated module over a complete (Noetherian) local ring.

Gorenstein homological dimensions and some duality results

2017 ◽  
Vol 10 (03) ◽  
pp. 1750048
Author(s):  
Fatemeh Mohammadi Aghjeh Mashhad
Keyword(s):  
Local Ring ◽  
Duality Theorem ◽  
Projective Dimension ◽  
Injective Dimension ◽  
Duality Results ◽  
Dualizing Complex ◽  
Matlis Duality ◽  
Homological Dimensions ◽  
Gorenstein Injective Dimension ◽  
Gorenstein Injective

Let [Formula: see text] be a local ring and [Formula: see text] denote the Matlis duality functor. Assume that [Formula: see text] possesses a normalized dualizing complex [Formula: see text] and [Formula: see text] and [Formula: see text] are two homologically bounded complexes of [Formula: see text]-modules with finitely generated homology modules. We will show that if G-dimension of [Formula: see text] and injective dimension of [Formula: see text] are finite, then [Formula: see text] Also, we prove that if Gorenstein injective dimension of [Formula: see text] and projective dimension of [Formula: see text] are finite, then [Formula: see text] These results provide some generalizations of Suzuki’s Duality Theorem and the Herzog–Zamani Duality Theorem.

Matlis Duality and Finiteness Properties of Generalized Local Cohomology Modules

2010 ◽  
Vol 17 (04) ◽  
pp. 637-646 ◽  
Author(s):  
Hero Saremi
Keyword(s):  
Local Cohomology ◽  
Projective Dimension ◽  
Regular Sequence ◽  
Local Cohomology Module ◽  
Local Cohomology Modules ◽  
Matlis Duality ◽  
Noetherian Dimension ◽  
Generalized Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

Let [Formula: see text] be an ideal of a commutative Noetherian local ring [Formula: see text] and M, N be two finitely generated R-modules such that M is of finite projective dimension n. Let t be a positive integer. We show that if there exists a regular sequence [Formula: see text] with [Formula: see text] and the i-th local cohomology module [Formula: see text] of N with respect to [Formula: see text] is zero for all i > t, then [Formula: see text], where D(-):= Hom R(-,E). Also, we prove that if N is a Cohen-Macaulay R-module of dimension d, then the generalized local cohomology module [Formula: see text] is co-Cohen-Macaulay of Noetherian dimension d. Finally, with an elementary proof, we show that [Formula: see text] is finite.

scholarly journals Appendix. Injective modules and Matlis duality

2007 ◽  
pp. 257-267
Author(s):  
Srikanth Iyengar ◽  
Graham Leuschke ◽  
Anton Leykin ◽  
Claudia Miller ◽  
Ezra Miller ◽  
...  
Keyword(s):  
Injective Modules ◽  
Matlis Duality

A Note on Local Cohomology

2008 ◽  
Vol 15 (01) ◽  
pp. 97-100 ◽  
Author(s):  
Amir Mafi ◽  
Hossein Zakeri
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Associated Primes ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Finitely Generated Module ◽  
Matlis Duality

A certain set of associated primes of the Matlis duality of any top local cohomology module of a complete filter local ring is characterized. Also, it is proved that the set of associated primes of a finitely generated module over a four-dimensional local ring is finite.

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