MATHEMATICA BOHEMICA, Vol. 129, No. 3, pp. 283-295 (2004)

Lexicographic extensions of dually residuated lattice ordered 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: Dually residuated lattice ordered monoids (\drl monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (\mv algebras, $BL$-algebras) and their non-commutative variants (\gmv algebras, pseudo $BL$-algebras). In the paper, lex-extensions and lex-ideals of \drl monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

Keywords: \drl monoid, ideal, lex-extension, lex-ideal, algebras of fuzzy logics

Classification (MSC2000): 06F05, 03G10, 06D35, 06F15

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