an abstract algebra problem

[patrickchensh]

R is a Ring.A is its ideal,which satisfies that for each r,there exist n,such that r^n belongs to A.which of the following may be possible pairs of (R,A)?(Z,2Z),(Z[X],<X^2+1>)

[vonLipwig]

This question doesn't make sense. As you've written it, A must be equal to R. (Try the condition with r = 1).

You'll get more useful help if you also say what you're tried, rather than just writing down a question and nothing else.