A ring R is called a right C-injective ring if every homomorphism from a closed right ideal of R to RR can be extended to one from RR to RR. 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.
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