On the LCM-Lattice of Powers of Monomial Ideal in Two Variables

Abstract

Let K be a field, and S = K[x1,...,xn] be a polynomial ring in n number of variables. To each monomial ideal I ⊂ S =K[x1,...,xn] one can construct lcm(I), the lcm-lattice of I. In this thesis, we classify different classes of monomial ideals for the case n = 2. In particular, we study the effect of powers on the lcm structure of a given ideal.”