IE-closed subcategories of commutative rings are torsion-free classes

Let C be a subcategory of the category of finitely generated R-modules over a commutative noetheian ring R. We prove that, if C is closed under images and extensions (which we call an IE-closed subcategory), then C is closed under submodules, and hence is a torsion-free class. This result complements... Show more