Semiprimitive ring

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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

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.

Definition

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:

Relation with other properties

Stronger properties

Weaker properties