Pseudocomplemented directoids. (English) Zbl 1212.06005

Chajda, Ivan

Commentat. Math. Univ. Carol. 49, No. 4, 533-539 (2008).

Summary: Directoids were introduced by J. Ježek and R. Quackenbush [Algebra Univers. 27, No. 1, 49–69 (1990; Zbl 0699.08002)] as a generalization of semilattices. 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.

MSC:

06A12	Semilattices
06D15	Pseudocomplemented lattices

Keywords:

commutative directoid; \(\lambda \)-lattice; pseudocomplement; Boolean elements

Citations:

Zbl 0699.08002