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Algebra universalis

, Volume 60, Issue 1, pp 63–90 | Cite as

Many-valued quantum algebras

  • Ivan Chajda
  • Radomír Halaš
  • Jan Kühr
Article

Abstract.

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.

2000 Mathematics Subject Classification:

06D35 06C15 03G25 

Keywords and phrases:

de Morgan algebra MV-algebra orthomodular lattice lattice effect algebra sectional antitone involution basic algebra MVQ-algebra 

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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Department of Algebra and Geometry, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic

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