= Jacobson radical
{wiki=Jacobson_radical}
The Jacobson radical is a concept that arises in the context of ring theory, a branch of abstract algebra. It is a particular ideal associated with a ring, which captures information about the ring's structure in relation to simple modules and semisimplicity. Here are the key points regarding the Jacobson radical: 1. **Definition**: The Jacobson radical \\( J(R) \\) of a ring \\( R \\) is defined as the intersection of all maximal left ideals of \\( R \\).
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