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Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 63-74
DOI: https://doi.org/10.7151/dmgaa.1076

DIRECT DECOMPOSITIONS OF DUALLY RESIDUATED LATTICE ORDERED MONOIDS

Jirí Rachnek Department of Algebra and Geometry, Faculty of Sciences, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic e-mail: rachunek@inf.upol.cz

Dana Salounová Department of Mathematical Methods in Economy, Faculty of Economics, VSB-Technical University of Ostrava, Sokolská 33, 701 21 Ostrava, Czech Republic e-mail:dana.salounova@vsb.cz

Abstract

The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.

Keywords: DRl-monoid, lattice-ordered monoid, ideal, normal ideal, polar, direct factor.

2000 Mathematics Subject Classification: 06F05; 06D35, 06F15, 03G10, 03G25, 20F60.

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Received 16 September 2003
Revised 18 February 2004