On distributive trices
Kiyomitsu Horiuchi, Andreja Tepavčević · Discussiones Mathematicae - General Algebra and Applications · 2001
A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them.A trice is a triple-semilattice, satisfying so called roundabout absorption laws.In this paper we investigate distributive trices.We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one.We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.