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Abstract Algebra

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Moderate

Jacobson Radical: Relation to Nilradical

ABSALG-CLE16H

Let $R$ be a commutative ring.

The Jacobson radical of $R$ is defined to be the intersection of all maximal ideals of $R$.

How is the Jacobson radical of $R$ related to the nilradical of $R$?

A

The Jacobson radical contains the nilradical.

B

The Jacobson radical is contained in the nilradical.

C

The Jacobson radical strictly contains the nilradical.

D

The Jacobson radical is strictly contained in the nilradical.