J-regular rings with injectivities

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A ring R is called a J-regular ring if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. It is proved that if R is J-regular, then (i) R is right n-injective if and only if every homomorphism from an n-generated small right ideal of R to Rᵣ can be extended to one from Rᵣ to Rᵣ; (ii) R is right FP-injective if and only if R is right (J, R)-FP-injective. Some known results are improved.