Abstract
Let be a non-empty collection of right ideals of a ring R . A right R-module X is called -injective provided each R-homomorphism ϕ: A → X with A in can be lifted to an R-homomorphism θ: R→X . If R is a commutative Noetherian ring and . = Spec R then every -injective R-module is injective. On the other hand, if R is a commutative Noetherian integral domain of finite global dimension and a non-empty collection of prime ideals of R containing the zero ideal such that every -injective R-module is injective then = Spec R.
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