Lattices embeddable in threegenerated lattices
Abstract
We prove that every finite lattice L can be embedded in a threegenerated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a model in which all cardinal numbers are accessible. Our results strengthen P. Crawley and R. A. Dean's 1959 results by adding finiteness, algebraicity, and completeness.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.03971
 Bibcode:
 2015arXiv151203971C
 Keywords:

 Mathematics  Rings and Algebras;
 06B99
 EPrint:
 11 pages, 3 figures