In the present paper we investigate the lattice of subvarieties of the variety of $\sqrt{^{\prime }}$\emph{\ quasi-MV algebras}. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra $\mathbf{D}_{r}$ is not finitely based, and we provide an infinite equational basis for the same variety.
The Lattice of Subvarieties of root ' quasi-MV Algebras
PAOLI, FRANCESCO;LEDDA, ANTONIO;GIUNTINI, ROBERTO
2010-01-01
Abstract
In the present paper we investigate the lattice of subvarieties of the variety of $\sqrt{^{\prime }}$\emph{\ quasi-MV algebras}. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra $\mathbf{D}_{r}$ is not finitely based, and we provide an infinite equational basis for the same variety.
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