 This is obviously a left-ideal over formula_1, and so is finitely generated by the leading coefficients of finitely many members of formula_38; say formula_41.Let formula_42 be the maximum of the set formula_43, and let formula_44 be the set of leading coefficients of members of formula_38, whose degree is formula_46.As before, the formula_44 are left-ideals over formula_1, and so are finitely generated by the leading coefficients of finitely many members of formula_38, say

with degrees formula_46.