Let A be a Noetherian ring, then show that any ring empimorphism is also injective.
Hint: consider a chain of ideals
As A is Noetherian, the chain of ideals becomes stationary, i.e for some n
Moreover we know that is also onto.
Suppose , then equals for some
Now as i.e
My question is why equals for some ?????? how do we get this?
and this line as i.e