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 Zpand 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.