reserve R for commutative Ring;
reserve A for non degenerated commutative Ring;
reserve I,J,q for Ideal of A;
reserve p for prime Ideal of A;
reserve M,M1,M2 for Ideal of A/q;

theorem Th32:
    for p be Ideal of A holds p is prime implies p is primary
    proof
      let p be Ideal of A;
      assume p is prime; then
      reconsider p as prime Ideal of A;
      for x,y be Element of A st x*y in p holds x in p or y in sqrt p
      proof
        let x,y be Element of A;
        assume x*y in p; then
A3:     x in p or y in p by RING_1:def 1;
        p c= sqrt p by TOPZARI1:20;
        hence thesis by A3;
      end;
      hence thesis by Def4;
    end;
