Coverings of [ MO n ] and minimal orthomodular lattices

• Autores: J. C. Carréga, Richard J. Greechie
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 4, 2008, págs. 427-459
• Idioma: inglés
• DOI: 10.1007/s00012-008-2078-9
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• Resumen

  • If T is an orthomodular lattice (OML), we denote by [T] the equational class generated by T. In this paper we characterize the finite OMLs T such that [T] covers some [MO n ]. These OMLs T are the non-modular OMLs such that all proper sub-OMLs of T are modular. An OML satisfying that last property is called minimal. There exist infinitely many minimal OMLs provided by quadratic spaces over finite fields. We describe them and give a new way to represent their Greechie diagrams in two separate parts. Other methods to obtain finite minimal OMLs are given.