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.
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