Final answer:
The set of all nilpotent elements in a commutative ring forms an ideal.
Step-by-step explanation:
In a commutative ring, the set of all nilpotent elements forms an ideal.
An ideal is a subset of a ring that is closed under addition, subtraction, and multiplication by elements of the ring.
To prove that the set of nilpotent elements forms an ideal, we need to show that it is closed under addition, negation, and multiplication by any element of the ring.