Lexicographic extensions of dually residuated lattice ordered monoids

Jiří Rachůnek; Dana Šalounová

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 3, page 283-295
  • ISSN: 0862-7959

Abstract

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Dually residuated lattice ordered monoids ( D R -monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ( M V -algebras, B L -algebras) and their non-commutative variants ( G M V -algebras, pseudo B L -algebras). In the paper, lex-extensions and lex-ideals of D R -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Lexicographic extensions of dually residuated lattice ordered monoids." Mathematica Bohemica 129.3 (2004): 283-295. <http://eudml.org/doc/249409>.

@article{Rachůnek2004,
abstract = {Dually residuated lattice ordered monoids ($DR\ell $-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ($MV$-algebras, $BL$-algebras) and their non-commutative variants ($GMV$-algebras, pseudo $BL$-algebras). In the paper, lex-extensions and lex-ideals of $DR\ell $-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Mathematica Bohemica},
keywords = {$DR\ell $-monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics; monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics},
language = {eng},
number = {3},
pages = {283-295},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lexicographic extensions of dually residuated lattice ordered monoids},
url = {http://eudml.org/doc/249409},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Lexicographic extensions of dually residuated lattice ordered monoids
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 3
SP - 283
EP - 295
AB - Dually residuated lattice ordered monoids ($DR\ell $-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ($MV$-algebras, $BL$-algebras) and their non-commutative variants ($GMV$-algebras, pseudo $BL$-algebras). In the paper, lex-extensions and lex-ideals of $DR\ell $-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
LA - eng
KW - $DR\ell $-monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics; monoid; ideal; lex-extension; lex-ideal; algebras of fuzzy logics
UR - http://eudml.org/doc/249409
ER -

References

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