# Ideals : Show that N is contained in P for each prime ideal, P of a commutative ring R.

Not what you're looking for? Search our solutions OR ask your own Custom question.

Show that N is contained in P for each prime ideal, P of a commutative ring R.

Where N is the set of all nilpotent elements. "a" is nilpotent if a^n=0 for some positive integer n. N itself is an ideal.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:40 pm ad1c9bdddfhttps://brainmass.com/math/ring-theory/ideals-prime-ideals-commutative-ring-55733

#### Solution Preview

Proof:

N is the set of all nilpotent elements. P is a prime ideal in a commutative ring R. We want to show ...

#### Solution Summary

It is shown that N is contained in P for each prime ideal, P of a commutative ring R.

$2.49