Affiliation:
1. Department of Mathematics, Lanzhou City University, Lanzhou 730070, China
Abstract
Let T be a compactly generated triangulated category. In this paper, the width and local homology dimension of an object X with respect to a homogeneous ideal a, widthR(a,X) and hd(a,X), respectively, are introduced. The local nature and some basic properties of widthR(a,X) and hd(a,X) are provided. In addition, we give an upper bound and lower bound of widthR(a,X). What is more, we give the relationship between the local homology dimension hd(a,X) and the arithmetic rank of a and dimR.
Reference22 articles.
1. Brodmann, M., and Sharp, R.Y. (1998). Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge Studies in Advanced Mathematics No. 60, Cambridge University Press.
2. Bounded complexes of flat modules;Foxby;J. Pure Appl. Algebra,1979
3. Lipman, J. (2002). Lectures on Local Cohomology and Duality. Local Cohomology and Its Applications, Dekker. Available online: https://www.taylorfrancis.com/chapters/edit/10.1201/9781482275766-2/lectures-local-cohomology-duality-joseph-lipman.
4. The Koszul complex and duality;Matlis;Comm. Algebra,1974
5. The higher properties of R-sequences;Matlis;J. Algebra,1978