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MV-algebra; modal operator; closure operator; residuated $\ell $-monoid; Heyting algebra
Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.
[1] Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many- valued Reasoning. Kluwer, Dordrecht, 2000. MR 1786097
[2] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. MR 1861369
[3] Macnab, D. S.: Modal operators on Heyting algebras. Algebra Univers. 12 (1981), 5–29. MR 0608645 | Zbl 0459.06005
[4] Rachůnek, J.: Modal operators on ordered sets. Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 24 (1985), 9–14. MR 0879015
[5] Rachůnek, J.: $DR\ell $-semigroups and MV-algebras. Czechoslovak Math. J. 48 (1998), 365–372. MR 1624268
[6] Rachůnek, J.: MV-algebras are categorically equivalent to a class of $DR\ell _{1(i)}$-semigroups. Math. Bohem. 123 (1998), 437–441. MR 1667115
[7] Rachůnek, J., Šalounová, D.: Local bounded commutative residuated $\ell $-monoids (submitted).
[8] Rachůnek, J., Švrček, F.: MV-algebras with additive closure operators. Acta Univ. Palacki. Olomuc., Fac. Rer. Mat., Math. 39 (2000), 183–189. MR 1826361
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