Minimal infinite submodule-closed subcategories

Details Minimal infinite submodule-closed subcategories Minimal infinite submodule-closed subcategories

2010-09-04

arxiv.org/abs/1009.0864v1

Mathematics

Representation Theory

Scientific paper

Let $\Lambda$ be an artin algebra. We are going to consider full subcategories of $\mod\Lambda$ 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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