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.

No reviews yet.

No comments yet.