1. Restricted Homological Dimensions of Complexes
- Author
-
Fangdi Kong and Dejun Wu
- Subjects
Noetherian ,Pure mathematics ,Mathematics::Commutative Algebra ,General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,010103 numerical & computational mathematics ,01 natural sciences ,Injective function ,Base change ,Mathematics::K-Theory and Homology ,Bounded function ,0101 mathematics ,Commutative property ,Associative property ,Mathematics - 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.
- Published
- 2018