J. Rachunek, Department of Algebra and Geometry, Faculty of Sciences, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: rachunek@inf.upol.cz; D. Salounova, Department of Mathematical Methods in Economy, Faculty of Economics, VSB-Technical University Ostrava, Sokolska 33, 701 21 Ostrava, Czech Republic, e-mail: dana.salounova@vsb.cz
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 (MSC 2000): 06F05, 03G10, 06D35, 06F15
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