We consider reduced Witt rings of finite chain length. We show there is a bound, in terms of the chain length and maximal signature, on the dimension of anisotropic, totally indefinite forms. From this we get the ascending chain condition on principal ideals and hence factorization of forms into products of irreducible forms.
Fitzgerald, Robert W. "Isotropy and Factorization in Reduced Witt Rings." (Mar 2001).