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.

About the authors

Dejun Wu

Lanzhou University of Technology

Author for correspondence.
Email: wudj@lut.cn
China, Lanzhou

Fangdi Kong

Lanzhou University of Technology

Email: wudj@lut.cn
China, Lanzhou

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