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Matematicheskie Zametki, 2018, Volume 103, Issue 5, Pages 667–679
DOI: https://doi.org/10.4213/mzm11990 (Mi mzm11990) 		 
Restricted Homological Dimensions of Complexes

Wu Dejun, Kong Fandy

Lanzhou University of Technology
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DOI: https://doi.org/10.4213/mzm11990
Abstract: 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.
Funding agency Grant number
National Natural Science Foundation of China 11761047
The first-named author was supported by the National Natural Science Foundation of China (No. 11761047).
Received: 15.04.2016
Revised: 13.01.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 703–712
DOI: https://doi.org/10.1134/S0001434618050036
Bibliographic databases:
Document Type: Article
UDC: 515.1
Language: Russian
Citation: Wu Dejun, Kong Fandy, “Restricted Homological Dimensions of Complexes”, Mat. Zametki, 103:5 (2018), 667–679; Math. Notes, 103:5 (2018), 703–712
Citation in format AMSBIB
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