Gorenstein Homological Algebra

2006 ◽  
pp. 75-86 ◽  
Author(s):  
Edgar Enochs ◽  
Overtoun Jenda
Keyword(s):  
Homological Algebra ◽  
Gorenstein Homological Algebra

scholarly journals Gorenstein homological algebra and universal coefficient theorems

2017 ◽  
Vol 287 (3-4) ◽  
pp. 1109-1155 ◽  
Author(s):  
Ivo Dell’Ambrogio ◽  
Greg Stevenson ◽  
Jan Šťovíček
Keyword(s):  
Homological Algebra ◽  
Gorenstein Homological Algebra

G-Gorenstein Complexes

2016 ◽  
Vol 119 (1) ◽  
pp. 14
Author(s):  
Maryam Akhavin ◽  
Eero Hyry
Keyword(s):  
Homological Algebra ◽  
Classical Notion ◽  
Fixed Dimension ◽  
Gorenstein Homological Algebra

We present in the context of Gorenstein homological algebra the notion of a "G-Gorenstein complex" as the counterpart of the classical notion of a Gorenstein complex. In particular, we investigate equivalences between the category of G-Gorenstein complexes of fixed dimension and the G-class of modules.

Ding w-Flat Modules and Dimensions

2018 ◽  
Vol 25 (02) ◽  
pp. 203-216
Author(s):  
Fuad Ali Ahmed Almahdi ◽  
Mohammed Tamekkante
Keyword(s):  
Exact Sequence ◽  
Homological Algebra ◽  
Projective Modules ◽  
Flat Module ◽  
Flat Dimension ◽  
Flat Modules ◽  
Gorenstein Projective Modules ◽  
Gorenstein Homological Algebra

The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-flat module if [Formula: see text] is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules … → P1 → P0 → P0 → P1 → … such that M ≅ Im(P0 → P0) and such that the functor HomR(−, F) leaves the sequence exact whenever F is w-flat. Several wellknown classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension (of modules and rings) and the existence of Ding w-flat precovers are also studied.

PERIODIC SHORT EXACT SEQUENCES AND PERIODIC PURE-EXACT SEQUENCES

2010 ◽  
Vol 09 (06) ◽  
pp. 859-870 ◽  
Author(s):  
SAMIR BOUCHIBA ◽  
MOSTAFA KHALOUI
Keyword(s):  
Exact Sequence ◽  
Finite Groups ◽  
Projective Module ◽  
Homological Algebra ◽  
Flat Module ◽  
Injective Modules ◽  
Flat Modules ◽  
Gorenstein Homological Algebra ◽  
Exact Sequences

Benson and Goodearl [Periodic flat modules, and flat modules for finite groups, Pacific J. Math.196(1) (2000) 45–67] proved that if M is a flat module over a ring R such that there exists an exact sequence of R-modules 0 → M → P → M → 0 with P a projective module, then M is projective. The main purpose of this paper is to generalize this theorem to any exact sequence of the form 0 → M → G → M → 0, where G is an arbitrary module over R. Moreover, we seek counterpart entities in the Gorenstein homological algebra of pure projective and pure injective modules.

Sign in / Sign up

Export Citation Format

Share Document