On fuzzy ideals of pseudo MV-algebras

Grzegorz Dymek

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 1, page 63-75
  • ISSN: 1509-9415

Abstract

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Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.

How to cite

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Grzegorz Dymek. "On fuzzy ideals of pseudo MV-algebras." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 63-75. <http://eudml.org/doc/276850>.

@article{GrzegorzDymek2008,
abstract = {Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.},
author = {Grzegorz Dymek},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {pseudo MV-algebra; fuzzy (prime, maximal) ideal; fuzzy ideal; prime ideal; maximal ideal},
language = {eng},
number = {1},
pages = {63-75},
title = {On fuzzy ideals of pseudo MV-algebras},
url = {http://eudml.org/doc/276850},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Grzegorz Dymek
TI - On fuzzy ideals of pseudo MV-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 1
SP - 63
EP - 75
AB - Fuzzy ideals of pseudo MV-algebras are investigated. The homomorphic properties of fuzzy prime ideals are given. A one-to-one correspondence between the set of maximal ideals and the set of fuzzy maximal ideals μ satisfying μ(0) = 1 and μ(1) = 0 is obtained.
LA - eng
KW - pseudo MV-algebra; fuzzy (prime, maximal) ideal; fuzzy ideal; prime ideal; maximal ideal
UR - http://eudml.org/doc/276850
ER -

References

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  1. [1] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. Zbl0084.00704
  2. [2] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327. Zbl0999.06011
  3. [3] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46. Zbl1177.06015
  4. [4] G. Dymek, Fuzzy prime ideals of pseudo-MV algebras, Soft Comput. 12 (2008), 365-372. Zbl1132.06006
  5. [5] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras: a non-commutative extension of MV-algebras, pp. 961-968 in: 'Proceedings of the Fourth International Symposium on Economic Informatics', Bucharest, Romania, May 1999. Zbl0985.06007
  6. [6] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135. 
  7. [7] C.S. Hoo and S. Sessa, Fuzzy maximal ideals of BCI and MV-algebras, Inform. Sci. 80 (1994), 299-309. Zbl0809.06012
  8. [8] Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Rev. Fuzzy Math.~ 1 (2006), 21-31. 
  9. [9] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. Zbl1012.06012
  10. [10] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. Zbl0139.24606

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