Yang, Gang Gorenstein projective, injective and flat complexes. (Chinese. English summary) Zbl 1240.16010 Acta Math. Sin., Chin. Ser. 54, No. 3, 451-460 (2011). Summary: It is shown in the paper that for a general associative ring \(R\), any complex \(C\) of \(R\)-modules is Gorenstein projective if and only if each \(R\)-module \(C^m\) is Gorenstein projective for all \(m\in\mathbb Z\); as immediate consequences of the result, Gorenstein projective dimensions of complexes are characterized. Furthermore, if \(C\) is an exact complex of \(R\)-modules such that this sequence remains exact when the functor \(\operatorname{Hom}(-,Q)\) is applied to it for any projective \(R\)-module \(Q\), then \(C\) is Gorenstein projective if and only if each \(\text{Ker}(\delta^m_C)\) is Gorenstein projective for all \(m\in\mathbb Z\). Similarly, Gorenstein injective and Gorenstein flat versions of all these results are given. Cited in 14 Documents MSC: 16E05 Syzygies, resolutions, complexes in associative algebras 16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 18G05 Projectives and injectives (category-theoretic aspects) 16E10 Homological dimension in associative algebras 16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras Keywords:Gorenstein flat complexes; Gorenstein injective complexes; Gorenstein projective complexes; preenvelopes; precovers PDFBibTeX XMLCite \textit{G. Yang}, Acta Math. Sin., Chin. Ser. 54, No. 3, 451--460 (2011; Zbl 1240.16010)