Prove that, for arbitrary short exact sequences a 0A PX 0, of modules over R with projective

Prove that, for arbitrary short exact sequences

 

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a 0→A P→X→ 0, of modules over R with projective for every n > 2 and B 0→B Q→Y → 0 modules P and Q, we have Tor, (X, Y) Torn-2 (A, B) Tor2(X, Y) Ker(a ß). a 0→A P→X→ 0, of modules over R with projective for every n > 2 and B 0→B Q→Y → 0 modules P and Q, we have Tor, (X, Y) Torn-2 (A, B) Tor2(X, Y) Ker(a ß).

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Let R be a commutative ring The functors TorRi A B are functors of two variable Rmodules A and B tha... View the full answer