Need help about Quotient Rings (Factor Rings)

[AAQIB IQBAL]

Suppose S is an Ideal of a Ring R
I want to verify the multiplication operation in the Factor Ring R/S which is
(S + a)(S + b) = (S + ab)
for this i Need to show that :
(S + ab) ≤ (S +a)(S + b)
please give me some idea about it
IT IS GIVEN AS DEFINITION IN THE BOOK I.N Herstein

 

[bpet]

It might help to consider a concrete example such as S=5Z with a=2 and b=3.