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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