Ideals of noncommutative D R -monoids

Jan Kühr

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 97-111
  • ISSN: 0011-4642

Abstract

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In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.

How to cite

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Kühr, Jan. "Ideals of noncommutative $DR\ell $-monoids." Czechoslovak Mathematical Journal 55.1 (2005): 97-111. <http://eudml.org/doc/30929>.

@article{Kühr2005,
abstract = {In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.},
author = {Kühr, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {dually residuated lattice ordered monoid; ideal; normal ideal; dually residuated lattice-ordered monoid; ideal; normal ideal},
language = {eng},
number = {1},
pages = {97-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ideals of noncommutative $DR\ell $-monoids},
url = {http://eudml.org/doc/30929},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Kühr, Jan
TI - Ideals of noncommutative $DR\ell $-monoids
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 97
EP - 111
AB - In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.
LA - eng
KW - dually residuated lattice ordered monoid; ideal; normal ideal; dually residuated lattice-ordered monoid; ideal; normal ideal
UR - http://eudml.org/doc/30929
ER -

References

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  6. 10.1007/s10012-000-0015-8, Southeast Asian Bull. Math. 24 (2000), 15–18. (2000) Zbl0988.08002MR1811209DOI10.1007/s10012-000-0015-8
  7. Ideals and congruences in generalized M V -algebras, Demonstratio Math. 33 (2000), 213–222. (2000) MR1769414
  8. A general theory of dually residuated lattice ordered monoids, PhD.  Thesis, Palacký Univ. Olomouc, 1996. (1996) 
  9. Prime ideals in autometrized algebras, Czechoslovak Math.  J. 112 (1987), 65–69. (1987) MR0875128
  10. 10.1023/A:1021766309509, Czechoslovak Math.  J. 52 (2002), 255–273. (2002) DOI10.1023/A:1021766309509
  11. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) MR0183797DOI10.1007/BF01360284
  12. 10.1007/BF01361218, Math. Ann. 167 (1966), 71–74. (1966) Zbl0158.02601MR0200364DOI10.1007/BF01361218

Citations in EuDML Documents

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  1. Jan Kühr, Dually residuated -monoids having no non-trivial convex subalgebras
  2. Dana Šalounová, Lex-ideals of DR -monoids and GMV-algebras
  3. Jan Kühr, Generalizations of pseudo MV-algebras and generalized pseudo effect algebras
  4. Jiří Rachůnek, Dana Šalounová, Direct product factors in GMV-algebras
  5. Filip Švrček, Interior and closure operators on bounded residuated lattice ordered monoids
  6. Jan Kühr, Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids
  7. Jan Kühr, Finite-valued dually residuated lattice-ordered monoids
  8. Jan Kühr, Jiří Rachůnek, Weak Boolean products of bounded dually residuated l -monoids
  9. Jiří Rachůnek, Dana Šalounová, Direct decompositions of dually residuated lattice-ordered monoids

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