**
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: ` 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 (MSC2000):** 06F05, 03G10, 06D35, 06F15

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]

*
© 2004–2010
FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
*