nil is a radical property
Every ring has a largest -ideal, which contains all other -ideals of . This ideal is written .
The sum of all nil ideals is nil (see proof http://planetmath.org/node/5650here), so this sum is the largest nil ideal in the ring.
Finally, if is the largest nil ideal in , and is an ideal of containing such that is nil, then is also nil (see proof http://planetmath.org/node/5650here). So by definition of . Thus contains no nil ideals.
|Title||nil is a radical property|
|Date of creation||2013-03-22 14:12:58|
|Last modified on||2013-03-22 14:12:58|
|Last modified by||mclase (549)|