A nonassociative extension of the class of distributive lattices
Ervin Fried, George Grätzer · Pacific Journal of Mathematics · 1973
Let Z = {0,1, 2} and define two binary operations Λ and V on Z as follows: 0Λl = 0,0vl = l,lΛ2 = l,lv2 = 2, 2 Λ 0 = 2,2 V 0 = 2, both operations are idempotent and commutative.This paper deals with the equational class Z generated by the algebra ζZ; Λ, V>.The class Z contains the class of all distributive lattices and Z is a subclass of the class of weakly associative lattices (trellis, T-lattice) in the sense of E. Fried and H. Skala.The purpose of this paper is to prove that Z shares the most important properties of the class of distributive lattices.