6.6.3 Ring homomorphism Definition 28: An everywhere function p R-s between two rings is a homomorphism if for all a, bEr (1)q(a+b)=q(a)+q(b), (2)q(ab)=(a)φ(b) An isomorphism is a bijective homomorphism. Two rings a are isomorphic if there is an isomorphism between them. If o: R-S is a ring homomorphism, then formula(1) implies that op is a group homomorphism between the groups r +]andS;+’ ◆ Hence it follows that ◆q(0)=0 s and p(-a)=-g(a) for all a∈R where OR and os denote the zero elements in R and s;6.6.3 Ring homomorphism  Definition 28: An everywhere function  : R→S between two rings is a homomorphism if for all a, bR,  (1)  (a + b) = (a) + (b),  (2)  (ab) =  (a)  (b)  An isomorphism is a bijective homomorphism. Two rings are isomorphic if there is an isomorphism between them.  If : R→S is a ring homomorphism, then formula (1) implies  that  is a group homomorphism between the groups [R; +] and [S; +’ ].  Hence it follows that   (0R) =0S and  (-a) = - (a) for all aR.  where 0R and 0S denote the zero elements in R and S;