Nil Radical Proof: Proving A's Ideal is Non-Empty

[JasonJo]

Homework Statement

Let A be any ideal of a commutative ring with unity R. Show that the nil radical of A, N(A)= {r|r^n is in A} where n is a positive integer, and n depends on r.

Homework Equations

The Attempt at a Solution

i don't quite understand the concept of the nil radical of A, what would be an element of this ideal? the unity element is in for every n a positive integer, so it's non empty but I'm still a little confused.

 

[AKG]

Is the equation you have a definition, or something you're asked to prove? If it's a definition, then what are you being asked to prove? If you're being asked to prove that equation, then what's the definition of N(A)?