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 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |