The Varieties Defined by P-compatible Identities of Modular Ortholattices

Abstract

In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices.

On some extensions of the class of MV-algebras

“…Theorem 4.3 ( [11]). The lattice of all nontrivial subvarieties of the variety MOL Ex ,that are generated be the sum of the set Ex(MOL) and the set of all identities of one variable in the type 2, 2, 1 , is isomorphic to the lattice (L(MOL)\T) × B.…”

“…Considering classes defined by regular identities is part of research on identities, in which the structure of terms creating them matters. Example of such identities are: normal, externally compatible, P-compatible, biregular, symmetric and many others (see for example [5,11,12,14,15,16,18,19,22,24]). In recent years, Płonka sums have been analyzed not only within universal algebra but also logic.…”