IE-closed subcategories of commutative rings are torsion-free classes
arXiv preprint, April 2023. Link: arXiv:2304.03260
Citation: H. Enomoto, IE-closed subcategories of commutative rings are torsion-free classes, arXiv:2304.032608.
Comment
Let $\mathcal{C}$ be a subcategory of the category of finitely generated $R$-modules over a commutative noetherian ring $R$. I proved that if $\mathcal{C}$ is closed under images and extensions, then $\mathcal{C}$ is closed under submodules, and thus becomes a torsion-free class.