Distributive associative near lattices
Dietmar Schweigert · Czech digital mathematics library · 1985
DISTRIBUTIVE ASSOCIATIVE NEAR LATTICES DIETMAR SCHWEIGERTThe aim of the note presented is to classify partially ordered sets by endowing them, in a natural wav, with two binary operations and thereby producing algebras.These algebras are formally similar to lattices and this parallel can be used to classify partially ordered sets in the usual algebraic way by way of homomorphisms, subalgebras, and direct products.A syntactical theory is also presented.In the note we study the lower part of the lattice of varieties of near lattices.The atoms of this lattice are the variety of distributive lattices generated by the two-element-lattice and a subvariety of distributive near lattices generated by a two-element-near-lattice with incomparable elements.