On some Algebraic Properties of the Ideals Associated to finite posets

Abstract

Let Ci be a chain 1 < ··· < i and P = Cα×Cβ×Cγ beafiniteposet. Toeachmaximal chain c of P we associate a monomial s(c) = si1 ···sit in polynomial ring k[s1,··· ,sn] over field k in n variables s1,··· ,sn. Consider an ideal IP which is generated by the monomial s(c) for all maximal chains c in P. A chain blocker B of a poset P is subset of P such that every maximal chain of P has non empty intersection with B and B is minimal with this property. In this thesis, we studied chain blockers of poset P for particular values of α, β and γ.