Grobner Bases and an Algorithm to Find the Monomials of an Ideal

Author

Thomas Enkosky

Date of Award

2004

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Henrik Bresinsky

Second Committee Member

David Bradley

Third Committee Member

Ali Ozluk

Abstract

This thesis gives background information on algebra and Gröbner bases to solve the following problem: Given an ideal I in the polynomial ring k[X₁,…,X_n], what monomials, if any, are in the ideal. This thesis shows that there is no loss in generality in assuming that the ideal is homogeneous. If the ideal is homogeneous we can use the properties of colon ideals and Gröbner basis to produce a term X such that there are monomials in I if and only if X is an element of I. We then present an algorithm, modeled after Buchberger's algorithm, that gives all the generators of the monomial subideal.

Recommended Citation

Enkosky, Thomas, "Grobner Bases and an Algorithm to Find the Monomials of an Ideal" (2004). Electronic Theses and Dissertations. 1090.
https://digitalcommons.library.umaine.edu/etd/1090