Cotorsion pairs induced by duality pairs

TY - JOUR

T1 - Cotorsion pairs induced by duality pairs

AU - Holm, Henrik

AU - Jørgensen, Peter

PY - 2009

Y1 - 2009

N2 - We introduce the notion of a duality pair and demonstrate how the left half of such a pair is“often“ covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules–introduced by Enochs and Jenda–is covering when the ground ring has a dualizing complex.

AB - We introduce the notion of a duality pair and demonstrate how the left half of such a pair is“often“ covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules–introduced by Enochs and Jenda–is covering when the ground ring has a dualizing complex.

KW - Auslander class

KW - Bass class

KW - Cotorsion pair

KW - Cover

KW - Duality pair

KW - Gorenstein flat dimension

KW - Gorenstein injective dimension

KW - Preenvelope

KW - Semi-Dualizing complex

UR - http://www.scopus.com/inward/record.url?scp=81755163149&partnerID=8YFLogxK

U2 - 10.1216/JCA-2009-1-4-621

DO - 10.1216/JCA-2009-1-4-621

M3 - Journal article

AN - SCOPUS:81755163149

SN - 1939-0807

VL - 1

SP - 621

EP - 633

JO - Journal of Commutative Algebra

JF - Journal of Commutative Algebra

IS - 4

ER -