Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek; Dana Šalounová

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 1, page 63-74
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Jiří Rachůnek, and Dana Šalounová. "Direct decompositions of dually residuated lattice-ordered monoids." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 63-74. <http://eudml.org/doc/287751>.

@article{JiříRachůnek2004,
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.},
author = {Jiří Rachůnek, Dana Šalounová},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {DRl-monoid; lattice-ordered monoid; ideal; normal ideal; polar; direct factor; Dually residuated lattice-ordered monoids; direct products; ideals},
language = {eng},
number = {1},
pages = {63-74},
title = {Direct decompositions of dually residuated lattice-ordered monoids},
url = {http://eudml.org/doc/287751},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Jiří Rachůnek
AU - Dana Šalounová
TI - Direct decompositions of dually residuated lattice-ordered monoids
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 1
SP - 63
EP - 74
AB - 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.
LA - eng
KW - DRl-monoid; lattice-ordered monoid; ideal; normal ideal; polar; direct factor; Dually residuated lattice-ordered monoids; direct products; ideals
UR - http://eudml.org/doc/287751
ER -

References

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