Nondegenerate ideals in the ring of polynomials

Kouchnirenko in 1976 shows a formula to compute the Milnor number of isolated singularity germs of functions in terms of the Newton polyhedron of the germ. Bivia-Ausina, Fukui and Saia in 2002 characerized a class of finite codimension ideals in the ring of formal power series which satisfy a Newton non degeneracy condition, moreover they showed how to compute the Hilbert Samuel multiplicity of such ideals in term of a convenient Newton polyhedron. On the other side Kouchnirenko shows a formula to compute the Milnor number of Newton non degenerate polinomilas in terms of its Newton polyhedron. The main objective this work is to develop a global study on the case of ideal of finite codimension in the ring of polynomials and generalize the results obtained by Bivià-Ausina, Fukui and Saia in 2002, with the determination of a class of ideals which satisfies a condition of Newton non-degeneracy and methods to the calculation of its multiplicities in terms of volumes of polyhedra Newton convenient. We shall also develope this study to the ideals of finite codimension in the class of Laurent polynomials. (AU)