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commutative directoid; $\lambda$-lattice; pseudocomplement; boolean elements
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.
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