C-Injective rings

Abstract

A ring [Formula: see text] is called a right C-injective ring if every homomorphism from a closed right ideal of [Formula: see text] to [Formula: see text] can be extended to one from [Formula: see text] to [Formula: see text]. It is clear that a right CS ring must be right C-injective. Left C-injective rings can be defined similarly. Properties of C-injective rings are explored in this paper. It is shown that a left C-injective ring may not be right C-injective and a right C-injective ring may not be right CS. Some extensions of C-injective rings are discussed.