Commutative rings with subinjective ideals

An ideal in a commutative ring is called subinjective if it is the homomorphic image of an injective module. It is proved that all ideals in a commutative ring are subinjective if and only if the ring is a direct sum of local rings with this property. Necessary and sufficient conditions are given for all ideals to be subinjective in the local case. In particular, this is the case for self-injective rings whose ideals are linearly ordered, and for local self-injective rings in which the maximal ideal has a nontrivial annihilator.
Bibliography: 7 titles.