Nordström Cederholm Ernst: Om nolldimensionella ideal och initialideal

Abstract:

It is shown that every zero-dimensional monomial ideal I is the initial ideal of I(Σ), where Σ is the set of multivariate degrees of the monomials outside I. Macaulay may have known this and possibly had a draft towards a proof that precede the concept of the Gr¨obner basis. Using modern terminology, a universal Gröbner basis to I(Σ) is provided. As a consequence, it is shown that the function that maps finite affine varieties V , to the set of multivariate degrees of the monomials outside the initial ideal of I(V ), stabilizes directly