# Nordström Cederholm Ernst: Om nolldimensionella ideal och initialideal

## Bachelor thesis presentation

**Time: **
Thu 2022-08-25 12.30 - 13.30

**Location: **
Albano, House 1, Room T

**Respondent: **
Nordström Cederholm Ernst

**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