One Class of Maximal Binary Monomials

The lattice of closed sets of monomials generated by a monomial of the form xy t over a finite field GF(k) is isomorphic to the lattice of divisors of k-1. If a monomial xy t generates a maximal element in that lattice, does it also generate a maximal element in the poset of closed sets generated by singleton binary monomials? This is the question studied in this paper. We have proven that over some finite fields xy 2 is a unique such monomial.