#### 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[X _{1},…,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