Let be a nilpotent ideal in a commutative ring , let and be modules and let : be an module homomorphism. Show that if the induced map is surjective, then is surjective.
Let be a nilpotent ideal in a commutative ring , let and be modules and let : be an module homomorphism. Show that if the induced map is surjective, then is surjective.
so for some since is surjective, we have: thus: which gives us: because