Krull-Schmidt decompositions for thick subcategories

Details Krull-Schmidt decompositions for thick subcategories Krull-Schmidt decompositions for thick subcategories

2005-07-08

arxiv.org/abs/math/0507181v2

Journal of Pure and Applied Algebra 210 (2007) 11-27

Mathematics

Algebraic Topology

Added more references, fixed some typos, to appear in Journal of Pure and Applied Algebra, 22 pages, 1 figure

Scientific paper

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.

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