MATHEMATICA BOHEMICA, Vol. 133, No. 3, pp. 299-311 (2008)

Modal operators on bounded residuated $ l$-monoids

Jiri Rachunek, Dana Salounova

J. Rachunek, Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail:; D. Salounova, Department of Mathematical Methods in Economy, Faculty of Economics, VSB-Technical University Ostrava, Sokolska 33, 701 21 Ostrava, Czech Republic, e-mail:

Abstract: Bounded residuated lattice ordered monoids ($\rl$-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo $\mv$-algebras (or, equivalently, $\gmv$-algebras) and pseudo $\bl$-algebras (and so, particularly, $\mv$-algebras and $\bl$-algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on $\mv$-algebras were studied by Harlenderova and Rachunek (2006) and on bounded commutative $\rl$-monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded $\rl$-monoids which need not be commutative and investigate their properties also for further derived algebras.

Keywords: residuated {\el}-monoid, residuated lattice, pseudo $\bl$-algebra, pseudo $\mv$-algebra

Classification (MSC2000): 06D35, 06F05

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