Jacobson radical: Difference between revisions
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Revision as of 05:35, 9 January 2007
Definition for commutative rings
Symbol-free definition
The Jacobson radical of a commutative unital ring is the intersection of all its maximal ideals.
Definition for noncommutative rings
The noncommutative case was considered by Jacobson while proving the famous Jacobson density theorem (Fill this in later).
Particular cases
Trivial ideal
A commutative unital ring whose Jacobson radical is trivial is termed a semisimple ring.