Dually residuated ℓ -monoids having no non-trivial convex subalgebras

Jan Kühr

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 103-108
  • ISSN: 0231-9721

Abstract

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In this note we describe the structure of dually residuated ℓ -monoids ( 𝐷𝑅 ℓ -monoids) that have no non-trivial convex subalgebras.

How to cite

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Kühr, Jan. "Dually residuated $\ell $-monoids having no non-trivial convex subalgebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 103-108. <http://eudml.org/doc/32502>.

@article{Kühr2006,
abstract = {In this note we describe the structure of dually residuated $\ell $-monoids ($\mathit \{DR\}\ell $-monoids) that have no non-trivial convex subalgebras.},
author = {Kühr, Jan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {$\mathit \{DR\}\ell $-monoid; $\mathit \{GPMV\}$-algebra; Archimedean property; DR-monoid; GBL-algebra; GPMV-algebra; GMV-algebra; simple algebra; convex subalgebra},
language = {eng},
number = {1},
pages = {103-108},
publisher = {Palacký University Olomouc},
title = {Dually residuated $\ell $-monoids having no non-trivial convex subalgebras},
url = {http://eudml.org/doc/32502},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Kühr, Jan
TI - Dually residuated $\ell $-monoids having no non-trivial convex subalgebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 103
EP - 108
AB - In this note we describe the structure of dually residuated $\ell $-monoids ($\mathit {DR}\ell $-monoids) that have no non-trivial convex subalgebras.
LA - eng
KW - $\mathit {DR}\ell $-monoid; $\mathit {GPMV}$-algebra; Archimedean property; DR-monoid; GBL-algebra; GPMV-algebra; GMV-algebra; simple algebra; convex subalgebra
UR - http://eudml.org/doc/32502
ER -

References

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  6. Kovář T.: A General Theory of Dually Residuated Lattice Ordered Monoids., Ph.D. thesis, Palacký University, Olomouc, , 1996. (1996) 
  7. Kühr J., Ideals of noncommutative D R ℓ -monoids, Czechoslovak Math. J. 55 (2005), 97–111. MR2121658
  8. Kühr J., On a generalization of pseudo MV-algebras, J. Mult.-Val. Log. Soft Comput. (to appear). MR2288689
  9. Kühr J., Generalizations of pseudo MV-algebras and generalized pseudo effect algebras, Submitted. Zbl1174.06330
  10. Swamy K. L. N., Dually residuated lattice ordered semigroups, . Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797

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