Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras
View through CrossRef
In this article we investigate the relations between the Gorenstein projective dimensions of [Formula: see text]-modules and their socles for [Formula: see text]-minimal Auslander–Gorenstein algebras [Formula: see text]. First we give a description of projective-injective [Formula: see text]-modules in terms of their socles. Then we prove that a [Formula: see text]-module [Formula: see text] has Gorenstein projective dimension at most [Formula: see text] if and only if its socle has Gorenstein projective dimension at most [Formula: see text] if and only if [Formula: see text] is cogenerated by a projective [Formula: see text]-module. Furthermore, we show that [Formula: see text]-minimal Auslander–Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
Title: Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras
Description:
In this article we investigate the relations between the Gorenstein projective dimensions of [Formula: see text]-modules and their socles for [Formula: see text]-minimal Auslander–Gorenstein algebras [Formula: see text].
First we give a description of projective-injective [Formula: see text]-modules in terms of their socles.
Then we prove that a [Formula: see text]-module [Formula: see text] has Gorenstein projective dimension at most [Formula: see text] if and only if its socle has Gorenstein projective dimension at most [Formula: see text] if and only if [Formula: see text] is cogenerated by a projective [Formula: see text]-module.
Furthermore, we show that [Formula: see text]-minimal Auslander–Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
Related Results
Quasi-Gorenstein projective and quasi-Gorenstein injective modules
Quasi-Gorenstein projective and quasi-Gorenstein injective modules
In this paper, we introduce quasi-Gorenstein projective and quasi-Gorenstein injective modules, study some of their properties and investigate their behavior with respect to short ...
GORENSTEIN MODULES AND GORENSTEIN MODEL STRUCTURES
GORENSTEIN MODULES AND GORENSTEIN MODEL STRUCTURES
AbstractGiven a complete hereditary cotorsion pair$(\mathcal{X}, \mathcal{Y})$, we introduce the concept of$(\mathcal{X}, \mathcal{X} \cap \mathcal{Y})$-Gorenstein projective modul...
Modules of finite Gorenstein flat dimension and approximations
Modules of finite Gorenstein flat dimension and approximations
AbstractWe study approximations of modules of finite Gorenstein flat dimension by (projectively coresolved) Gorenstein flat modules and modules of finite flat dimension. These appr...
Differential graded vertex Lie algebras
Differential graded vertex Lie algebras
This is the continuation of the study of differential graded (dg) vertex algebras defined in our previous paper [Caradot et al., “Differential graded vertex operator algebras and t...
A note on Gorenstein projective and Gorenstein flat modules
A note on Gorenstein projective and Gorenstein flat modules
We prove that all Gorenstein projective modules are Gorenstein flat if and only each Gorenstein projective module has finite Gorenstein flat dimension. As applications, some charac...
Quantum B-algebras
Quantum B-algebras
Abstract
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic...
Relations between L-algebras and other logical algebras
Relations between L-algebras and other logical algebras
In this paper, by considering the notion of L-algebra, we show that there are relations between L-algebras and some of other logical algebras such as residuated lattices, MTL-alge...
Teorema de Gabriel para álgebras de caminhos de tipo finito
Teorema de Gabriel para álgebras de caminhos de tipo finito
O objetivo deste texto e, simplesmente, explorar diversos tópicos da teoria de representações de álgebras de dimensão finita. O teorema de Gabriel, que trata do tipo de representaç...