Semiprimitive ring

Name
A semiprimitive ring or ring with trivial Jacobson radical is sometimes termed a semisimple ring, although the latter term is usually reserved for a semisimple Artinian ring.

Symbol-free definition
A commutative unital ring is said to be semiprimitive or to have trivial Jacobson radical if it satisfies the following equivalent conditions:


 * Its Jacobson radical (i.e., the intersection of all its maximal ideals) is the zero ideal
 * It is a subdirect product of fields i.e., it can be embedded inside a direct product of fields

Stronger properties

 * Field
 * Semisimple Artinian ring