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. 
@article{MZM_2018_103_5_a2,
     author = {Wu Dejun and Kong Fandy},
     title = {Restricted {Homological} {Dimensions} of {Complexes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {667--679},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a2/}
}
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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/