English

Indecomposables live in all smaller lengths

Representation Theory 2012-01-12 v2 Category Theory

Abstract

Let k be an algebraically closed field and A a finite dimensional associative k-algebra. We prove that there is no gap in the lengths of indecomposable A-modules of finite length. The analogous result holds for an abelian k-linear category C if the endomorphism algebras of the simples are k.

Keywords

Cite

@article{arxiv.0904.4609,
  title  = {Indecomposables live in all smaller lengths},
  author = {Klaus Bongartz},
  journal= {arXiv preprint arXiv:0904.4609},
  year   = {2012}
}

Comments

correction of an error in part c) of lemma 9; minor changes (style)

R2 v1 2026-06-21T12:56:22.604Z