Restricted Homological Dimensions of Complexes

Wu Dejun, Kong Fandy

Lanzhou University of Technology

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.

UDC: 515.1

Received: 15.04.2016
Revised: 13.01.2017

DOI: 10.4213/mzm11990

 English version: Mathematical Notes, 2018, 103:5, 703–712

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