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On some extensions of the class of MV-algebras. (English) Zbl 1373.06013

Summary: In the present paper we will ask for the lattice \(L(\mathbf{MV}_{\mathrm{Ex}})\) of subvarieties of the variety defined by the set \(\mathrm{Ex}(\mathbf{MV})\) of all externally compatible identities valid in the variety \(\mathbf{MV}\) of all MV-algebras. In particular, we will find all subdirectly irreducible algebras from the classes in the lattice \(L(\mathbf{MV}_{\mathrm{Ex}})\) and give syntactical and semantical characterization of the class of algebras defined by \(P\)-compatible identities of MV-algebras.

MSC:

06D35 MV-algebras
08B15 Lattices of varieties
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