Many-valued quantum algebras

• Autores: Ivan Chajda, Radomír Halas, Jan Kühr
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 60, Nº. 1, 2009, págs. 63-90
• Idioma: inglés
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• Resumen

  • We deal with algebras $${\bf A} = (A, \oplus, \neg, 0)$$ of the same signature as MV-algebras which are a common extension of MV-algebras and orthomodular lattices, in the sense that (i) A bears a natural lattice structure, (ii) the elements a for which $$\neg a$$ is a complement in the lattice form an orthomodular sublattice, and (iii) subalgebras whose elements commute are MV-algebras. We also discuss the connections with lattice-ordered effect algebras and prove that they form a variety.