ON GEOMETRICAL REPRESENTATION OF VARIETIES OF LATTICES

摘要

Our main aim is to derive the embedding properties of modular lattice within its variety, into an algebraic Lattice. We extend here that every lattice which is either algebraic modular spatial or bi-algebraic is strongly spatial. Hermann and Roddy derived that every modular lattice embeds into some algebraic and spatial lattice. We show here that every n-distributive lattice embeds within its variety. It is illustrated by an example that only those lattice with a least and greatest element can be embedded which is join semi-distributive. The main derivation is that for every positive integer n, every n-distributive lattice is embedded within its variety which generalises word problem derived by C. Herrmann.