Structure of Orthomodular Lattices

Abstract

Let ‵L be an ortholattice and let a, b ∈ L. The element (a ∧ b′)∧ b will be called the skew join $a\dot{ \vee }b$ of the elements a,b; the skew meet of a,b is defined dually as the element $a\dot{ \wedge }b = (a \vee b\prime ) \wedge b$. The two skew operations $\dot{ \vee },\dot{ \wedge }$ give rise to a new algebra ${{L}^{ \cdot }} = (L,\dot{ \vee }, \dot{ \wedge },\prime ,0,1)$ which will be called the Boolean skew lattice associated with ‵L.