The following are alternative characterizations of the Jacobson radical :
The Jacobson radical can also be defined for non-unital rings. To do this, we first define a binary operation on the ring by for all . Then is a monoid, and the Jacobson radical is defined to be the largest ideal of such that is a group. If is unital, this is equivalent to the definitions given earlier.
|Date of creation||2013-03-22 12:36:11|
|Last modified on||2013-03-22 12:36:11|
|Last modified by||yark (2760)|