English

Minimal infinite submodule-closed subcategories

Representation Theory 2010-09-07 v1

Abstract

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

Keywords

Cite

@article{arxiv.1009.0864,
  title  = {Minimal infinite submodule-closed subcategories},
  author = {Claus Michael Ringel},
  journal= {arXiv preprint arXiv:1009.0864},
  year   = {2010}
}
R2 v1 2026-06-21T16:09:33.762Z