Epimorphisms in Certain Varieties of Algebras

We prove a lemma which, under restrictive conditions, shows that epimorphisms in V are surjective if this is true for epimorphisms from irreducible members of V . This lemma is applied to varieties of orthomodular lattices which are generated by orthomodular lattices of bounded height, and to varieties of orthomodular lattices which are generated by orthomodular lattices which are the horizontal sum of their blocks. The lemma can also be applied to obtain known results for discriminator varieties. Mathematics Subject Classifications (2000): 06C15, 03G12, 08B25. Key words: epimorphism, ortholattice, orthomodular lattice.

• Type: Journal
• Year: 2000
• Where: ORDER
• Authors: Gunter Bruns, John Harding
• Keywords: Irreducible Members, ORDER 2000, Orthomodular Lattice, Restrictive Conditions