REALIZATION OF A CERTAIN CLASS OFSEMI-GROUPS AS VALUE SEMI-GROUPS OFVALUATIONS

Given a well-ordered semi-group Ґ with a minimal systemof generators of ordinal type at most wn 1 and of rational rank r ,which satisfies a positivity and increasing condition, we construct azero-dimensional valuation centered on the ring of polynomials withT variables such that the semi-group of the values of the polynomialring is equal to Ґ. The construction uses a generalization of Favreand Jonsson s version of MacLane s sequence of key-polynomials[3].