Near λ-lattices

Abstract

By a near λ-lattice is meant an upper λ-semilattice where is dened a partialbinary operation x∧y with respect to the induced order whenever x,y has a common lowerbound. Alternatively, a near λ-lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near λ-lattices is a quasi-variety. A λ-semilattice A = (A;∨) is said to have sectional (antitone) involutions if foreach a ∈A there exists an (antitone) involution on [a,1], where 1 is the greatest element of A.If this antitone involution is a complementation, A is called an ortho λ-semilattice.We characterize these near λ-lattices by certain identities.