7.11. Let - M - N- M2-70 be an exact sequence of R-modules. (This may be...

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Question

Answer 1

Answer #1

The solution is given below. We show that the given homomorphism is actually an isomorphism. Using this, we show that the sequence splits.

let the diagram be as below: به رو میدن و و - M, o M. MOM, I Meto first prove that f: N the we M w , will 0 M₂ is an R-module

Havever, as the diagram commutes, Im (f) = MO{0}. - 7 BENst f(z) – y = f(p). - y = f(Z-R) =) y E Im (f). af is surjective. fi

Answer 2

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