#### Thesis Title

### Powers of Monomial Ideals

#### Date of Graduation

Spring 1999

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Kishor Shah

#### Abstract

We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an ideal I. We calculate the Hilbert Polynomial of certain monomial ideals. Ou approach is algebraic as well as geometric.

#### Subject Categories

Mathematics

#### Copyright

© Rhonda S Haynes

#### Recommended Citation

Haynes, Rhonda S., "Powers of Monomial Ideals" (1999). *MSU Graduate Theses*. 870.

https://bearworks.missouristate.edu/theses/870

**Dissertation/Thesis**