On ideals of lattice ordered monoids

Milan Jasem

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 4, page 369-387
  • ISSN: 0862-7959

Abstract

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In the paper the notion of an ideal of a lattice ordered monoid A is introduced and relations between ideals of A and congruence relations on A are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.

How to cite

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Jasem, Milan. "On ideals of lattice ordered monoids." Mathematica Bohemica 132.4 (2007): 369-387. <http://eudml.org/doc/250250>.

@article{Jasem2007,
abstract = {In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.},
author = {Jasem, Milan},
journal = {Mathematica Bohemica},
keywords = {lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice-ordered monoid},
language = {eng},
number = {4},
pages = {369-387},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On ideals of lattice ordered monoids},
url = {http://eudml.org/doc/250250},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Jasem, Milan
TI - On ideals of lattice ordered monoids
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 4
SP - 369
EP - 387
AB - In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
LA - eng
KW - lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice-ordered monoid
UR - http://eudml.org/doc/250250
ER -

References

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  9. Dually Residuated Lattice Ordered Monoids, Doctoral Thesis, Palacký Univ., Olomouc, 2003. (2003) Zbl1066.06008MR2070377
  10. 10.1007/s10587-005-0006-0, Czech. Math. J. 55 (2005), 97–111. (2005) MR2121658DOI10.1007/s10587-005-0006-0
  11. Prime ideals and polars in DRl-monoids and pseudo BL-algebras, Math. Slovaca 53 (2003), 233–246. (2003) MR2025020
  12. Prime ideals in autometrized algebras, Czech. Math. J. 37 (1987), 65–69. (1987) 
  13. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284
  14. Lex-ideals of DRl-monoids and GMV-algebras, Math. Slovaca 53 (2003), 321–330. (2003) MR2025465

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