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Restricted Homological Dimensions of Complexes

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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.

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Authors and Affiliations

  1. Lanzhou University of Technology, Lanzhou, China

    Dejun Wu & Fangdi Kong

Authors
  1. Dejun Wu
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  2. Fangdi Kong
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Correspondence to Dejun Wu.

Additional information

Published in Russian in Matematicheskie Zametki, 2018, Vol. 103, No. 5, pp. 667–679.

The text was submitted by the authors in English.

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Wu, D., Kong, F. Restricted Homological Dimensions of Complexes. Math Notes 103, 703–712 (2018). https://doi.org/10.1134/S0001434618050036

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  • DOI: https://doi.org/10.1134/S0001434618050036

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