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arXiv:math/0507181 [math.AT]AbstractReferencesReviewsResources

Krull-Schmidt decompositions for thick subcategories

Sunil K. Chebolu

Published 2005-07-08, updated 2006-07-25Version 2

Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these categories, it is shown that the thick ideals of small objects decompose uniquely into indecomposable thick ideals. We also discuss some consequences of these decomposition results. In particular, it is shown that all these decompositions respect K-theory.

Comments: Added more references, fixed some typos, to appear in Journal of Pure and Applied Algebra, 22 pages, 1 figure
Journal: Journal of Pure and Applied Algebra 210 (2007) 11-27
Categories: math.AT
Subjects: 55P42, 18E30, 16W30
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