Lemma 46.8.9. Let A be a ring.
\text{Pext}^ i_ A(M, N) = 0 for i > 0 whenever N is pure injective,
\text{Pext}^ i_ A(M, N) = 0 for i > 0 whenever M is pure projective, in particular if M is an A-module of finite presentation,
\text{Pext}^ i_ A(M, N) is also the ith cohomology module of the complex \mathop{\mathrm{Hom}}\nolimits _ A(P_\bullet , N) where P_\bullet is a pure projective resolution of M.
Comments (0)