The Gabriel-Roiter filtration of the Ziegler spectrum
  Inclusion preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum which is indexed by all Gabriel-Roiter measures. Another application is a compactness result for the set of subcategories of finitely presented modules that are closed under submodules. 
Henning Krause, Mike Prest
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