English

Torsion-simple objects in abelian categories

Representation Theory 2023-12-08 v1 Commutative Algebra Category Theory

Abstract

We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties, and then proceed to investigate the notion in various contexts, such as the category of modules over an artin algebra or a commutative noetherian ring, and the category of quasi-coherent sheaves over the projective line.

Keywords

Cite

@article{arxiv.2312.04384,
  title  = {Torsion-simple objects in abelian categories},
  author = {Sergio Pavon},
  journal= {arXiv preprint arXiv:2312.04384},
  year   = {2023}
}

Comments

17 pages. Comments are welcome

R2 v1 2026-06-28T13:44:06.300Z