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A non-commutative generalization of M V -algebras

Jiří Rachůnek

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 2, page 255-273
  • ISSN: 0011-4642

How to cite

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Rachůnek, Jiří. "A non-commutative generalization of $MV$-algebras." Czechoslovak Mathematical Journal 52.2 (2002): 255-273. <http://eudml.org/doc/30697>.

@article{Rachůnek2002,
author = {Rachůnek, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {MV-algebra; generalized MV-algebra; dually residuated lattice ordered monoid},
language = {eng},
number = {2},
pages = {255-273},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A non-commutative generalization of $MV$-algebras},
url = {http://eudml.org/doc/30697},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Rachůnek, Jiří
TI - A non-commutative generalization of $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 255
EP - 273
LA - eng
KW - MV-algebra; generalized MV-algebra; dually residuated lattice ordered monoid
UR - http://eudml.org/doc/30697
ER -

References

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  1. Foundations of the Theory of Quasigroups and Loops, Nauka, Moscow, 1967. (Russian) (1967) MR0218483
  2. Groupes et Anneaux Réticulés, SpringerVerlag, Berlin-Heidelberg-New York, 1977. (1977) MR0552653
  3. A Course in Universal Algebra, Springer-Verlag, Berlin-Heidelberg-New York, 1981. (1981) MR0648287
  4. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  5. A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–80. (1959) Zbl0093.01104MR0122718
  6. Free lattice-ordered abelian groups and varieties of M V -algebras, Proc. IX. Latin. Amer. Symp. Math. Log., Part 1, Not. Log. Mat. 38 (1993), 113–118. (1993) Zbl0827.06012MR1332526
  7. Lattice-Ordered Groups (Advances and Techniques), A. M. W. Glass and W. Charles Holland (eds.), Kluwer Acad. Publ., Dordrecht-Boston-London, 1989. (1989) Zbl0705.06001MR1036072
  8. M V -algebras, ideals and semisimplicity, Math. Japon. 34 (1989), 563–583. (1989) Zbl0677.03041MR1005257
  9. The Theory of Lattice Ordered Groups, Kluwer Acad. Publ., Dordrecht-Boston-London, 1994. (1994) MR1369091
  10. A general theory of dually residuated lattice ordered monoids, Thesis, Palacký University Olomouc, 1996. (1996) 
  11. Interpretation of A F C * -algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1986), 15–63. (1986) Zbl0597.46059MR0819173
  12. M V -algebras are categorically equivalent to bounded commutative B C K -algebras, Math. Japon. 31 (1986), 889–894. (1986) Zbl0633.03066MR0870978
  13. 10.1023/A:1022801907138, Czechoslovak Math. J. 48(123) (1998), 365–372. (1998) MR1624268DOI10.1023/A:1022801907138
  14. M V -algebras are categorically equivalent to a class of D R l 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  15. Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797
  16. 10.1007/BF01364335, Math. Ann. 160 (1965), 64–71. (1965) MR0191851DOI10.1007/BF01364335
  17. 10.1007/BF01361218, Math. Ann. 167 (1966), 71–74. (1966) Zbl0158.02601MR0200364DOI10.1007/BF01361218

Citations in EuDML Documents

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  1. Magdalena Wojciechowska-Rysiawa, IF-filters of pseudo-BL-algebras
  2. Grzegorz Dymek, On fuzzy ideals of pseudo MV-algebras
  3. Andrzej Walendziak, On maximal ideals of pseudo-BCK-algebras
  4. Jiří Rachůnek, Connections between ideals of non-commutative generalizations of M V -algebras and ideals of their underlying lattices
  5. Jiří RACHŮNEK, Dana ŠALOUNOVÁ, Approximation Spacesin Non-commutative Generalizations of M V -algebras
  6. Anatolij Dvurečenskij, States on unital partially-ordered groups
  7. Jiří Rachůnek, Radicals in non-commutative generalizations of MV-algebras
  8. P. Emanovský, Jiří Rachůnek, A non commutative generalization of -autonomous lattices
  9. Grzegorz Dymek, Noetherian and Artinian pseudo MV-algebras
  10. Ivan Chajda, Miroslav Kolařík, Remarks on pseudo MV-algebras

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