injective resolution
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2018 ◽  
Vol 62 (3) ◽  
pp. 625-640
Author(s):  
Thế Cu’ò’ng Nguyễn

AbstractThe algebraic EHP sequences, algebraic analogues of the EHP sequences in homotopy theory, are important tools in algebraic topology. This note will outline two new proofs of the existence of the algebraic EHP sequences. The first proof is derived from the minimal injective resolution of the reduced singular cohomology of spheres, and the second one follows Bousfield's idea using the loop functor of unstable modules.



2012 ◽  
Vol 19 (03) ◽  
pp. 433-446
Author(s):  
Mohsen Aghajani ◽  
Hossein Zakeri

Let R be a commutative Noetherian ring. In this paper, we study those finitely generated R-modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a module a G-Gorenstein module. Characterizations of G-Gorenstein modules are given and a class of such modules is determined. It is shown that the class of G-Gorenstein modules strictly contains the class of Gorenstein modules. Also, we provide a Gorenstein injective resolution for a balanced big Cohen-Macaulay R-module. Finally, using the notion of a G-Gorenstein module, we obtain characterizations of Gorenstein and regular local rings.



2010 ◽  
Vol 53 (7) ◽  
pp. 1715-1721
Author(s):  
ZhaoYong Huang ◽  
Yao Wang
Keyword(s):  


2009 ◽  
Vol 81 (1) ◽  
pp. 24-44 ◽  
Author(s):  
Lars Winther Christensen ◽  
Janet Striuli ◽  
Oana Veliche


2009 ◽  
Vol 16 (01) ◽  
pp. 95-101
Author(s):  
Kazem Khashyarmanesh

Let R be a Gorenstein local ring. We show that for a balanced big Cohen–Macaulay module M over R, the Cousin complex [Formula: see text] provides a Gorenstein injective resolution of M. Also, over a d-dimensional Gorenstein local ring R with maximal ideal 𝔪, we show that [Formula: see text], the dth local cohomology module of M with respect to 𝔪, is Gorenstein injective if (a) M is a balanced big Cohen–Macaulay R-module, or (b) M ∈ G(R), where G(R) is the Auslander's G-class of R.



2007 ◽  
Vol 35 (11) ◽  
pp. 3713-3750
Author(s):  
C.-Y. Jean Chan ◽  
I.-Chiau Huang


1998 ◽  
Vol 26 (2) ◽  
pp. 447-451 ◽  
Author(s):  
Hisaaki Fujita


1990 ◽  
Vol 32 (2) ◽  
pp. 173-188 ◽  
Author(s):  
R. Y. Sharp ◽  
M. Yassi

Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [19, Section 2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n ∈ N0 (we use N0 to denote the set of non-negative integers),Cohen–Macaulay rings can be characterized in terms of the Cousin complex: A is a Cohen–Macaulay ring if and only if C(A) is exact [19, (4.7)]. Also, the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring (see [19,(5.4)]).



1989 ◽  
Vol 65 ◽  
pp. 41 ◽  
Author(s):  
Edgar E. Enochs
Keyword(s):  


1988 ◽  
Vol 112 ◽  
pp. 53-61 ◽  
Author(s):  
Edgar Enochs

Let C, C′ and C″ be abelian categories where C and C′ have enough injectives and let F: C → C′, G: C′ → C″ be additive covariant functors. Then for an object X of C, let C(X) be the complex associated with an injective resolution of X. Grothendieck gets a first quadrant spectral sequence by taking an injective resolution of the complex F(C(X)) and applying G to the associated double complex.



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