Finiteness of the number of minimal atoms in Grothendieck categories
arXiv:1503.02116 · doi:10.1016/j.jalgebra.2019.03.003
Abstract
For a Grothendieck category having a noetherian generator, we prove that there are only finitely many minimal atoms. This is a noncommutative analogue of the fact that every noetherian scheme has only finitely many irreducible components. It is also shown that each minimal atom is represented by a compressible object.
10 pages