Near λ-lattices
Ivan Chajda, Miroslav Kolařík · Kyungpook mathematical journal · 2007
By a near -lattice is meant an upper -semilattice where is defined a parti binary operation with respect to the induced order whenever , has a common lower bound. Alternatively, a near -lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near -lattices is a quasivariety. A -semilattice is said to have sectional (antitone) involutions if for each there exists an (antitone) involution on [, 1], where 1 is the greatest element of . If this antitone involution is a complementation, is called an ortho -semilattice. We characterize these near -lattices by certain identities.