Further Properties of Ext
The Ext functor exhibits some convenient properties, useful in computations.
- Exti
R(A, B) = 0 for i > 0 if either B is injective or A projective.
- A converse also holds: if Ext1
R(A, B) = 0 for all A, then Exti
R(A, B) = 0 for all A, and B is injective; if Ext1
R(A, B) = 0 for all B, then Exti
R(A, B) = 0 for all B, and A is projective.
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