The lattice of subvarieties of \({\sqrt{^\prime}}\) quasi-MV algebras (Q609648)

\(\sqrt{'}\) quasi-MV-algebras were introduced in [\textit{R. Giuntini}, \textit{A. Ledda} and \textit{F. Paoli}, ``Expanding quasi-MV-algebras by a quantum operator'', Stud. Log. 87, No. 1, 99--128 (2007; Zbl 1127.06008)] as an axiomatization of the equational theory of the algebra of density operators endowed with connectives of quantum Łukasiewicz disjunctions and square root of negation. The paper under review is a continuation of this research. The main contribution is the solution to a long-standing open problem: the authors show that the variety generated by the standard disk algebra \(\mathbb D_r\) is not finitely based (Theorem 40) and they provide an infinite equational basis for the variety.