Vol. 49, No. 1, 1973

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A nonassociative extension of the class of distributive lattices

Ervin Fried and George Grätzer

Vol. 49 (1973), No. 1, 59–78
Abstract

Let Z = {0,1,2} and define two binary operations and V on Z as follows: 0Λ1 = 0,0 vl = 1,1 2 = 1, lv2 = 2,2 0 = 2,2 0 = 2, both operations are idempotent and commutative. This paper deals with the equational class Z generated by the algebra Z;,∨⟩. 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.

Mathematical Subject Classification
Primary: 06A20
Milestones
Received: 19 July 1972
Revised: 15 October 1972
Published: 1 November 1973
Authors
Ervin Fried
George Grätzer