It is shown that if a bound f ( i ) f(i) is placed on the degrees of the elements in some basis of an ideal A i {A_i} in the polynomial ring k [ X 1 , ⋯ , X n ] k[{X_1}, \cdots ,{X_n}] over the field k , i = 0 , 1 , 2 , ⋯ k,i = 0,1,2, \cdots , then a bound can be placed on the length of a strictly ascending chain A 0 > A 1 > ⋯ {A_0} > {A_1} > \cdots . Moreover one could explicitly write down a formula for a bound g n {g_n} in terms of f and n.