Local bounded commutative residuated ℓ -monoids

Jiří Rachůnek; Dana Šalounová

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 395-406
  • ISSN: 0011-4642

Abstract

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Bounded commutative residuated lattice ordered monoids ( R ℓ -monoids) are a common generalization of, e.g., B L -algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative R ℓ -monoids are investigated.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Local bounded commutative residuated $\ell $-monoids." Czechoslovak Mathematical Journal 57.1 (2007): 395-406. <http://eudml.org/doc/31137>.

@article{Rachůnek2007,
abstract = {Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Czechoslovak Mathematical Journal},
keywords = {residuated $\ell $-monoid; residuated lattice; $BL$-algebra; $MV$-algebra; local $R\ell $-monoid; filter; residuated lattice; BL-algebra; MV-algebra; local R-monoid; filter},
language = {eng},
number = {1},
pages = {395-406},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local bounded commutative residuated $\ell $-monoids},
url = {http://eudml.org/doc/31137},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Local bounded commutative residuated $\ell $-monoids
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 395
EP - 406
AB - Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of, e.g., $BL$-algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative $R\ell $-monoids are investigated.
LA - eng
KW - residuated $\ell $-monoid; residuated lattice; $BL$-algebra; $MV$-algebra; local $R\ell $-monoid; filter; residuated lattice; BL-algebra; MV-algebra; local R-monoid; filter
UR - http://eudml.org/doc/31137
ER -

References

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  1. 10.1007/s00012-003-1822-4, Alg. Univ. 50 (2003), 83–106. (2003) MR2026830DOI10.1007/s00012-003-1822-4
  2. 10.1142/S0218196703001511, Intern. J.  Alg. Comp. 13 (2003), 437–461. (2003) MR2022118DOI10.1142/S0218196703001511
  3. Algebraic Foundations of Many-Valued Reasoning, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. (2000) MR1786097
  4. New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. (2000) MR1861369
  5. 10.1007/s00233-005-0545-6, Semigroup Forum. 72 (2006), 191–206. (2006) MR2216089DOI10.1007/s00233-005-0545-6
  6. 10.1007/s00500-005-0473-0, Soft Comput. 10 (2006), 212–218. (2006) DOI10.1007/s00500-005-0473-0
  7. Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998. (1998) MR1900263
  8. A survey of residuated lattices, In: Ordered Algebraic Structures, J.  Martinez (ed.), Kluwer Acad. Publ., Dordrecht, 2002, pp. 19–56. (2002) MR2083033
  9. 10.1023/A:1022801907138, Czechoslovak Math.  J. 48 (1998), 365–372. (1998) MR1624268DOI10.1023/A:1022801907138
  10. M V -algebras are categorically equivalent to a class of  D R ℓ 1 ( i ) semigroups, Math. Bohemica 123 (1998), 437–441. (1998) MR1667115
  11. A duality between algebras of basic logic and bounded representable D R ℓ -monoids, Math. Bohemica 126 (2001), 561–569. (2001) MR1970259
  12. Boolean deductive systems of bounded commutative residuated ℓ -monoids, Contrib. Gen. Algebra 16 (2005), 199–207. (2005) MR2166959
  13. 10.1007/s10587-006-0053-1, Czechoslovak Math.  J. 56 (2006), 755–763. (2006) MR2291772DOI10.1007/s10587-006-0053-1
  14. Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures, Math. Slovaca. 56 (2006), 223–233. (2006) MR2229343
  15. 10.1007/BF01360284, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797DOI10.1007/BF01360284
  16. 10.1007/BF01361218, Math. Ann. 167 (1966), 71–74. (1966) Zbl0158.02601MR0200364DOI10.1007/BF01361218
  17. Mathematics Behind Fuzzy Logic, Physica-Verlag, Heidelberg-New York, 1999. (1999) Zbl0940.03029MR1716958
  18. Local B L -algebras, Multip. Val. Logic 6 (2001), 229–250. (2001) MR1817445

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