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
    for M be maximal Ideal of A, n be non zero Nat holds M||^n in PRIMARY(A,M)
    proof
      let M be maximal Ideal of A, n be non zero Nat;
      reconsider q = M||^n as proper Ideal of A by Lm1;
      sqrt q is maximal by Th15; then
      reconsider Mn = M||^n as primary Ideal of A by Th39;
      Mn is M-primary by Th15;
      hence thesis;
    end;
