Closed Sets of Monomials in Two Variables Generated by Singletons

摘要

We consider closed sets of monomials in two variables over a finite field GF(k), generated by singletons. For a two-variable monomial m, the closed set of monomials generated by m is defined as a set of terms of type {m} over {x, y}. We describe the structure of the poset of closed sets of monomials generated by monomials of the form xy(p) and determine minimal and maximal idempotent binary monomials.