properties of the Jacobson radical
Let . We claim that is left invertible:
Since is surjective, for some . Since , we know is left invertible, so there exists such that . Then we have
So as required.
Let be rings. Then .
Let be a (surjective) projection. By the previous theorem, .
Similarly let be a (surjective) projection. We see that .
Now take . Note that and . Hence as required.
|Title||properties of the Jacobson radical|
|Date of creation||2013-03-22 12:49:43|
|Last modified on||2013-03-22 12:49:43|
|Last modified by||yark (2760)|