Geodesic
Simple weakly transitive modal algebras
Algebra i logika, Tome 49 (2010) no. 3, pp. 346-365

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Weakly transitive modal algebras are studied. It is proved that the class of simple weakly transitive algebras coincides with the class of simple $DL$-algebras. A full description is given for finitely generated simple $DL$-algebras together with their embeddings. As a consequence, it is shown that the varieties of weakly transitive algebras and of $DL$-algebras are not weakly amalgamable, and that modal logics $wK4$ and $DL$ do not possess the weak interpolation property.
Keywords: weakly transitive modal algebra, $DL$-algebra, weakly amalgamable variety, weak interpolation property. 
@article{AL_2010_49_3_a2,
     author = {A. V. Karpenko and L. L. Maksimova},
     title = {Simple weakly transitive modal algebras},
     journal = {Algebra i logika},
     pages = {346--365},
     publisher = {mathdoc},
     volume = {49},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_3_a2/}
}
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A. V. Karpenko; L. L. Maksimova. Simple weakly transitive modal algebras. Algebra i logika, Tome 49 (2010) no. 3, pp. 346-365. http://geodesic.mathdoc.fr/item/AL_2010_49_3_a2/