Geodesic
Restricted Homological Dimensions of Complexes
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 667-679.

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We define and study the notions of restricted Tor-dimension and Ext-dimension for unbounded complexes of left modules over associative rings. We show that, for a right (respectively, left) homologically bounded complex, our definition agrees with the small restricted flat (respectively, injective) dimension defined by Christensen et al. Furthermore, we show that the restricted Tor-dimension defined in this paper is a refinement of the Gorenstein flat dimension of an unbounded complex in some sense. In addition, we give some results concerning restricted homological dimensions under a base change over commutative Noetherian rings.
Keywords: DG-projective (injective) complex, module-finite. 
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Wu Dejun; Kong Fandy. Restricted Homological Dimensions of Complexes. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 667-679. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a2/

[1] L. L. Avramov, H.-B. Foxby, “Homological dimensions of unbounded complexes”, J. Pure Appl. Algebra, 71 (1991), 129–155 | DOI | MR

[2] O. Veliche, “Gorenstein projective dimension for complexes”, Trans. Amer. Math. Soc., 358:3 (2006), 1257–1283 | DOI | MR

[3] J. Asadollahi, S. Salarian, “Gorenstein injective dimension for complexes and Iwanaga–Gorenstein rings”, Comm. Algebra, 34:8 (2006), 3009–3022 | DOI | MR

[4] L. W. Christensen, H.-B. Foxby, A. Frankild, “Restricted homological dimensions and Cohen–Macaulayness”, J. Algebra, 251 (2002), 479–502 | DOI | MR

[5] A. Iacob, “Gorenstein flat dimension of complexes”, J. Math. Kyoto Univ., 49:4 (2009), 817–842 | DOI | MR

[6] E. E. Enochs, O. M. G. Jenda, J. Xu, “Orthogonality in the category of complexes”, Math. J. Okayama Univ., 38 (1996), 25–46 | MR

[7] D. Bennis, “Rings over which the class of Gorenstein flat modules is closed under extensions”, Comm. Algebra, 37:3 (2009), 855–868 | DOI | MR

[8] H. Holm, “Gorenstein homological dimensions”, J. Pure Appl. Algebra, 189 (2004), 167–193 | DOI | MR

[9] L. W. Christensen, S. Sather-Wagstaff, “Transfer of Gorenstein dimensions along ring homomorphisms”, J. Pure Appl. Algebra, 214:6 (2010), 982–989 | DOI | MR

[10] D. Apassov, “Almost finite modules”, Comm. Algebra, 27:2 (1999), 919–931 | DOI | MR

[11] L. W. Christensen, Gorenstein Dimensions, Lecture Notes in Math., 1747, Springer-Verlag, Berlin, 2000 | DOI | MR | Zbl