On fuzzy ideals of pseudo MV-algebras

• Autorzy: Grzegorz Dymek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pseudo MV-algebra; fuzzy (prime, maximal) ideal

Kategorie tematyczne

• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 63-75

Daty

wydano

2008

otrzymano

2007-02-23

poprawiono

2007-04-04

Twórcy

autor

Grzegorz Dymek

• Institute of Mathematics and Physics, University of Podlasie, 3 Maja 54, 08-110 Siedlce, Poland

Bibliografia

• [1] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
• [2] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327.
• [3] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46.
• [4] G. Dymek, Fuzzy prime ideals of pseudo-MV algebras, Soft Comput. 12 (2008), 365-372.
• [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.
• [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.
• [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.
• [10] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.

Identyfikatory

DOI

10.7151/dmgaa.1135