TY - JOUR

T1 - A NOTE ON DG-GORENSTEIN INJECTIVE COVERS

AU - Iacob, A.

N1 - Publisher Copyright:
© 2022, Comenius University in Bratislava. All rights reserved.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - We consider a ring R such that the class of Gorenstein injective modules is closed under direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch(R) if and only if every complex of Gorenstein injective modules is dg-Gorenstein injective. In particular, when R is commutative noetherian with a dualizing complex, we obtain the following result: the class of dg-Gorenstein injective complexes is covering if and only if R is Gorenstein.

AB - We consider a ring R such that the class of Gorenstein injective modules is closed under direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch(R) if and only if every complex of Gorenstein injective modules is dg-Gorenstein injective. In particular, when R is commutative noetherian with a dualizing complex, we obtain the following result: the class of dg-Gorenstein injective complexes is covering if and only if R is Gorenstein.

KW - dg-Gorenstein injective complex

KW - Gorenstein injective module

UR - http://www.scopus.com/inward/record.url?scp=85123918304&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85123918304

SN - 0862-9544

VL - 91

SP - 19

EP - 25

JO - Acta Mathematica Universitatis Comenianae

JF - Acta Mathematica Universitatis Comenianae

IS - 1

ER -