# On fuzzy ideals of pseudo MV-algebras

Discussiones Mathematicae - General Algebra and Applications (2008)

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

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topGrzegorz 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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- [2] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327. Zbl0999.06011
- [3] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46. Zbl1177.06015
- [4] G. Dymek, Fuzzy prime ideals of pseudo-MV algebras, Soft Comput. 12 (2008), 365-372. Zbl1132.06006
- [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] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135.
- [7] C.S. Hoo and S. Sessa, Fuzzy maximal ideals of BCI and MV-algebras, Inform. Sci. 80 (1994), 299-309. Zbl0809.06012
- [8] Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Rev. Fuzzy Math.~ 1 (2006), 21-31.
- [9] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. Zbl1012.06012
- [10] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. Zbl0139.24606

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