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The Jacobson radical of a ring with identity is defined by one of the following equivalent ways:
The Jacobson radical is named for Nathan Jacobson , who first defined and studied the Jacobson radical.
If ring does not have identity, then the definition of the Jacobson ideal is more involved. First define the binary operation on by for all . Then is a semigroup with an identity element. Then the Jacobson radical is defined to be the largest ideal of such that is a subgroup of .
Cite this web-page as:
Štefan Porubský: The Jacobson radical.