Title of article :
Depth and Dimension for Triangulated Categories
Author/Authors :
Wang ، Li Department of Mathematics - College of Economics - Northwest Normal University , Liu ، Zhongkui Department of Mathematics - College of Economics - Northwest Normal University , Yang ، Xiaoyan Department of Mathematics - College of Economics - Northwest Normal University
Abstract :
A new notion of depth of an object X with respect to a homogeneous ideal a, depthR(a, X), is introduced for a compactly generated triangulated category T ; the local nature and some basic properties of depthR(a, X) are provided. What’s more, we give a computation of the dimension dimR X of objects in T , and prove that if (R,m) is a graded local ring, then depthR(a, X) ≤ dimR X +inf X for every ohomologically finite object X in T .
Keywords :
Triangulated category , Depth , Dimension ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
