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http://dx.doi.org/10.4134/BKMS.2016.53.2.551

DEPTH FOR TRIANGULATED CATEGORIES  

Liu, Yanping (Department of Mathematics, Northwest Normal University)
Liu, Zhongkui (Department of Mathematics, Northwest Normal University)
Yang, Xiaoyan (Department of Mathematics, Northwest Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 551-559 More about this Journal
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, 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;
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