Some results on special binomial ideals

Abstract

The main goal of this paper is to characterize a particular class of ideals whose structure can still be interpreted directly from their generators: binomial ideals having a finite number of binomials generators in a polynomial ring k[x] = k[x_1 , ..., x_n ]. More in details, we associate to every binomial ideal a homogeneous linear system constructed on its generators. We call it Toric System because it supplies us Toric Ideals given as elimination ideals. We observe that the constructed Toric Ideals depend only on the rank of a matrix that is solution of the Toric System. In addition, we define a binomial principal generator and then, we give some results for the case of a particular class of binomial ideals.