TWO CLASSES OF HOMOMORPHISMS IN MODULE CATEGORIES

Abstract

In a category R-Mod a homomorphism α:A → B is called projective if α factors through every epimorphism with B as image. Injective homomorphisms are defined dually. Some properties of such homomorphisms are derived, and it is shown that the hereditariness of the ring R is equivalent to some conditions which can be simply stated in terms of projective and injective homomorphisms.