Minimal infinite submodule-closed subcategories

2010/09/04 by Claus Michael Ringel, Ringel, Claus Michael
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1009.0864

arxiv created 2010/09/04 · arxiv updated 2010/09/07

Abstract

Let Λ be an artin algebra. We are going to consider full subcategories of \modΛ closed under finite direct sums and under submodules with infinitely many isomorphism classes of indecomposable modules. The main result asserts that such a subcategory contains a minimal one and we exhibit some striking properties of these minimal subcategories. These results have to be considered as essential finiteness conditions for such module categories.

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