This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions
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.
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