Gorenstein injective, projective and flat (pre)covers

E. Enochs, S. Estrada and A. Iacob

Received: April 25, 2013;   Revised: January 21, 2014;   Accepted: March 13, 2014

Abstract.   We prove that if the ring R is left noetherian and if the class of Gorenstein injective modules, GI, is closed under filtrations, then GI is precovering. We extend this result to the category of complexes. We also prove that when R is commutative noetherian and such that the character modules of Gorenstein injective modules are Gorenstein flat, the class of Gorenstein injective complexes is both covering and enveloping. This is the case when the ring is commutative noetherian with a dualizing complex. The second part of the paper deals with Gorenstein projective and flat complexes. We prove the existence of special Gorenstein projective precovers over commutative noetherian rings of finite Krull dimension.

Keywords:  Gorenstein injective (pre)cover; envelope; Gorenstein flat cover; Gorenstein projective precover.  

AMS Subject classification: Primary:  18G25, 18G35, 13D02  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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