The blowing up of a monomial ideal in the affine space is non necessarily normal. It is covered by affine charts determined by certain semigroup algebras. We explain how one can generalize this example to define toric varieties without the normality assumption. Gonzalez-Sprinberg proved that the Semple-Nash modification on a toric variety is described by the blowing up of certain monomial ideal. We study some properties of this modification in terms of monomial valuations. This is a joint work with B. Teissier.