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Direct product factors in $GMV$-algebras

Jiří Rachůnek - Dana Šalounová

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Rok, strany / Year, pages: 2005, 399-407

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Publikované / Published: 0000-00-00

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$GMV$-algebras are non-commutative generalizations of $MV$-algebras and by A. Dvurečenskij they can be represented as intervals of unital lattice ordered groups. Moreover, they are polynomially equivalent to dually residuated $\ell$-monoids ($DR\ell$-monoids) from a certain variety of $DR\ell$-monoids. In the paper, using these correspondences, direct product factors in $GMV$-algebras are introduced and studied and the lattices of direct factors are described. Further, the polars of projectable $GMV$@-algebras are described.

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