Injectives for ring monomorphisms with accessible images

Abstract

The injectives in the category of associative rings and homomorphisms with accessible images are investigated.It is shown that every such ring has an identity and is a direct sum of finitely many indecomposable injectives.The indecomposable injectives are shown to be simple when they are algebras over fields other than Zp and in the remaining characteristic p case to have only three ideals.A necessary and sufficient condition is obtained for certain finite direct sums of indecomposable injectives to be injective.