Many-valued quantum algebras.

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. [ABSTRACT FROM AUTHOR]