PROPERTIES OF THE FORMAL CONTEXT OF ORTHOMODULAR LATTICES

Abstract

Let $L$ be a finite Orthomodular Lattice and $T$ be the Formal Context of $L$. Then, considering $T$ as a binary symmetric matrix, we find the determinant of the formal context of the atomic amalgam $B_n+B_m$ of two Boolean algebras $\mathbf{B_{n}}$ and $\mathbf{B_{m}}$ consisting of $n$ and $m$ atoms, respectively using the Schur complement formula\cite{p28}. We present the proofs of some preliminary results on the determinant of the context table of the Boolean algebra $B_{n}$ and the characteristic polynomial of $B_{n}$. These preliminary results are used in many applications in graph theory.