Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(2): 551-559

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.551

Copyright © The Korean Mathematical Society.

Depth for triangulated categories

Yanping Liu, Zhongkui Liu, and Xiaoyan Yang

Northwest Normal University, Northwest Normal University, Northwest Normal University

Abstract

Recently a construction of local cohomology functors for compactly generated triangulated categories admitting small coproducts is introduced and studied by Benson, Iyengar, Krause, Asadollahi and their coauthors. Following their idea, we introduce the depth of objects in such triangulated categories and get that when $(R,\mathfrak{m})$ is a graded-commutative Noetherian local ring, the depth of every cohomologically bounded and cohomologically finite object is not larger than its dimension.

Keywords: triangulated category, depth, dimension

MSC numbers: 18E30, 13C15