DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

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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.

References

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Received 16 September 2003
Revised 18 February 2004


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