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arXiv · 1009.0864

Minimal infinite submodule-closed subcategories

Claus Michael Ringel
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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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Claus Michael Ringel. 2010-09-04. Minimal infinite submodule-closed subcategories. https://arxiv.org/abs/1009.0864

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