On the Structure of a Generalization of Weakly Associative Lattices

Abstract

The concept of weakly associative lattices (i.e. relational systems with a reflexive and antisymmetric relation \(\leq\), in which for each pair of elements there exist a least upper and a greatest lower bound) was introduced in [3] and [5]. In [4] WU-systems are defined, i.e. weakly associative lattices with the unique bound property, and their equivalence with projective planes is described. In this paper we introduce WU\(_{\lambda}\)-systems, and discuss their relation to symmetric \(2\)-\((v,k,\lambda)\) designs equipped with a special “loop-free” mapping.