Morita contexts and unitary ideals of rings

In this talk I will prove that if two associative rings are connected by a Morita context with surjective mappings, then these rings have isomorphic quantales of unitary ideals. I will also show that the quotient rings by ideals that correspond to each other under that isomorphism are connected by a Morita context with surjective mappings. Finally I will consider how annihilators and two-sided socles behave under that isomorphism.