
theorem
for n being Prime,
    p being non constant Element of the carrier of Polynom-Ring(Z/n)
holds Z/n, (Polynom-Ring Z/n)/({p}-Ideal) are_disjoint
proof
let n be Prime,
    p be non constant Element of the carrier of Polynom-Ring Z/n;
set F = Z/n, KR = (Polynom-Ring Z/n)/({p}-Ideal);
X: [#] F = the carrier of F & [#] KR = the carrier of KR;
(the carrier of Z/n) /\
      (the carrier of (Polynom-Ring (Z/n))/({p}-Ideal)) = {} by Disj1;
hence thesis by X,FIELD_2:def 1;
end;
