Abstract:Directoids as a generalization of semilattices were introduced by J. Je\v {z}ek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.
Keywords: commutative directoid, $\lambda $-lattice, pseudocomplement, boolean elements
AMS Subject Classification: 06A12, 06D15, 06C15, 06A99