Noetherian and Artinian pseudo MV-algebras

• Autorzy: Grzegorz Dymek
• Języki publikacji: EN

Abstrakty

EN

The notions of Noetherian pseudo MV-algebras and Artinian pseudo MV-algebras are introduced and their characterizations are established. Characterizations of them via fuzzy ideals are also given.

Słowa kluczowe

EN

pseudo MV-algebra; (fuzzy) ideal; Noetherian (Artinian) pseudo MV-algebra

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: 2
• Strony: 209-225

Daty

wydano

2008

otrzymano

2008-02-05

poprawiono

2008-04-09

poprawiono

2008-04-22

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. Di Nola, A. Dvurečenskij and J. Jakubík, Good and bad infinitesimals, and states on pseudo MV-algebras, Order 21 (2004), 293-314.
• [3] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327.
• [4] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46.
• [5] G. Dymek, Fuzzy prime ideals of pseudo MV-algebras, Soft Computing 12 (2008), 365-372.
• [6] G. Dymek, On fuzzy ideals of pseudo MV-algebras, Discussiones Mathematicae - General Algebra and Applications 28 (2008), 63-75.
• [7] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras: a non-commutative extension of MV-algebras, p. 961-968 in: 'The Proceedings of the Fourth International Symposium on Economic Informatics', Bucharest, Romania 1999.
• [8] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135.
• [9] Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Review. Fuzzy Math. 1 (2006), 21-31.
• [10] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273.
• [11] J. Rachůnek, Prime spectra of non-commutative generalizations of MV-algebras, Algebra Univ. 48 (2002), 151-169.
• [12] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287.
• [13] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.

Identyfikatory

DOI

10.7151/dmgaa.1144