Giuntini, Roberto Weakly linear quantum MV-algebras. (English) Zbl 1093.06011 Algebra Univers. 53, No. 1, 45-72 (2005). Quantum MV-algebras (QMV-algebras) were introduced by the author in “Quantum MV algebras” [Stud. Log. 56, No. 3, 393–417 (1996; Zbl 0854.03057)] as a non-lattice-theoretical generalization of both MV-algebras and orthomodular lattices. An important example is the system \(E({\mathcal H})\) of all Hermitian operators of a Hilbert space \({\mathcal H}\) between the zero operators and the identity. In general, every po-group \(G\) with a positive element \(u\) gives another example \(G[0,u] =\{g \in G:\;0\leq g \leq u\}\), where \(a\oplus b = a+b\) if \(a+b \leq u\) otherwise \(a\oplus b = u\), of a GMV-algebra. The accent in the paper is on weakly linear QMV-algebras for which the author studies a finite basis for the variety generated by the class of weakly linear QMV-algebras. Finally, three open problems are formulated. Reviewer: Anatolij Dvurečenskij (Bratislava) Cited in 4 Documents MSC: 06D35 MV-algebras 06C15 Complemented lattices, orthocomplemented lattices and posets 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:quantum MV-algebra; orthomodular lattice Citations:Zbl 0854.03057 PDFBibTeX XMLCite \textit{R. Giuntini}, Algebra Univers. 53, No. 1, 45--72 (2005; Zbl 1093.06011) Full Text: DOI