So here is the part of exercise 14 of chapter 1 that has been bothering me:
Let $A$ be a commutaive ring with identity. Let $\Sigma $ be the set of ideals with the property that every element in them is a zero divisor. Show that maximal elements of $\Sigma $ are prime.
I saw many online solutions, but I found them all to be flawed proofs. It would be great to hear a valid proof from somebody here.
Thank you a lot.
Here is one proof that I think is flawed :
Criticism: why is it true that all elements of $(m,x) $ are zero divisors?