Paper detail

Minimal infinite submodule-closed subcategories

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.