Hi:

I have the Jacobson radical of a ring R defined as J(R) = {a R: aR is r.q.r}, where r.q.r stands for right quasi-regular. If S is another ring and f:R-->S is an isomorphism of R onto S, I want to prove (I know, there's no need) that J(R)f = J(S).

Could somebody give me a hint? Thanks in advance.