reserve p,q for Rational;
reserve g,m,m1,m2,n,n1,n2 for Nat;
reserve i,i1,i2,j,j1,j2 for Integer;
reserve R for Ring, F for Field;

theorem
for R being Ring, S being R-homomorphic Ring holds Char S divides Char R
proof
let R be Ring, S be R-homomorphic Ring;
set n = Char S, m = Char R;
reconsider n1=n,m1=m as Element of INT.Ring by INT_1:def 2;
(the Homomorphism of R,S) * canHom_Int(R) = canHom_Int(S) by Th83;
then ker(canHom_Int(R)) c= ker(canHom_Int(S)) by Th68;
then {m1}-Ideal c= ker(canHom_Int(S)) by Th81;
then {m1}-Ideal c= {n1}-Ideal by Th81;
then n1 divides m1 by RING_2:19;
hence thesis by Lm3;
end;
