Thread: Ring homomorphism

If we have a ring homomorphism

f:R to R'

i am wondering for a subring of R which is by definition an ideal, will the homomorphic properties of the initial ring homomorphism be maintained between the setf(r)= R' and some subring S with the apllication of f, eg f(s)?

I don't understand your question! Also, a subring is not necessarily an ideal!