Title: Krull-Schmidt decompositions for thick subcategories
Author: Sunil Chebolu
Email address: schebolu@uwo.ca
AMS classifictaion numbers: Primary: 55p42; Secondary: 18E30
Address: Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7
Abstract: Following Krause, we prove Krull-Schmidt theorems for thick subcategories of  various triangulated categories:  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.  Some consequences of these decomposition results 
are also discussed. In particular, it is shown that all these decompositions respect $K$-theory