Noetherian and Artinian pseudo MV-algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 209-225.

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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.
Keywords: pseudo MV-algebra, (fuzzy) ideal, Noetherian (Artinian) pseudo MV-algebra
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Dymek, Grzegorz. Noetherian and Artinian pseudo MV-algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 209-225. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a5/

[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.