On Different Classes of Monomial Ideals Associated to Lcm-Lattices

Abstract

Let K be a field, and a ring of polynomial S = K[x1,...,xn] in n numbers of variables. To each monomial ideal I in S we associate the lcm-lattice denoted by L(I). Consider I and J be two monomial ideals such that, L(I) is isomorphic to L(J). In this thesis we discuss different classes of above mentioned ideals such that L(In) and L(Jn) are isomorphic for different values of n. In the end we state few conjectures.