Noetherian and Artinian pseudo MV-algebras
Grzegorz Dymek
Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008), p. 209-225 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:276844 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1144,
     author = {Grzegorz Dymek},
     title = {Noetherian and Artinian pseudo MV-algebras},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {28},
     year = {2008},
     pages = {209-225},
     zbl = {1195.06006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1144}
}

Grzegorz Dymek. Noetherian and Artinian pseudo MV-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 209-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1144/

[000] [1] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. | Zbl 0084.00704

[001] [2] A. Di Nola, A. Dvurečenskij and J. Jakubík, Good and bad infinitesimals, and states on pseudo MV-algebras, Order 21 (2004), 293-314. | Zbl 1081.06010

[002] [3] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327. | Zbl 0999.06011

[003] [4] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46. | Zbl 1177.06015

[004] [5] G. Dymek, Fuzzy prime ideals of pseudo MV-algebras, Soft Computing 12 (2008), 365-372. | Zbl 1132.06006

[005] [6] G. Dymek, On fuzzy ideals of pseudo MV-algebras, Discussiones Mathematicae - General Algebra and Applications 28 (2008), 63-75. | Zbl 1157.06006

[006] [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. | Zbl 0985.06007

[007] [8] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135.

[008] [9] Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Review. Fuzzy Math. 1 (2006), 21-31.

[009] [10] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. | Zbl 1012.06012

[010] [11] J. Rachůnek, Prime spectra of non-commutative generalizations of MV-algebras, Algebra Univ. 48 (2002), 151-169. | Zbl 1058.06015

[011] [12] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287. | Zbl 1086.06011

[012] [13] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. | Zbl 0139.24606