# Noetherian and Artinian pseudo MV-algebras

Discussiones Mathematicae - General Algebra and Applications (2008)

- Volume: 28, Issue: 2, page 209-225
- ISSN: 1509-9415

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topGrzegorz Dymek. "Noetherian and Artinian pseudo MV-algebras." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 209-225. <http://eudml.org/doc/276844>.

@article{GrzegorzDymek2008,

abstract = {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.},

author = {Grzegorz Dymek},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {pseudo MV-algebra; (fuzzy) ideal; Noetherian (Artinian) pseudo MV-algebra; Noetherian pseudo MV-algebras; Artinian pseudo MV-algebras},

language = {eng},

number = {2},

pages = {209-225},

title = {Noetherian and Artinian pseudo MV-algebras},

url = {http://eudml.org/doc/276844},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Grzegorz Dymek

TI - Noetherian and Artinian pseudo MV-algebras

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2008

VL - 28

IS - 2

SP - 209

EP - 225

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/276844

ER -

## References

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- [2] A. Di Nola, A. Dvurečenskij and J. Jakubík, Good and bad infinitesimals, and states on pseudo MV-algebras, Order 21 (2004), 293-314. Zbl1081.06010
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- [4] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46. Zbl1177.06015
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- [6] G. Dymek, On fuzzy ideals of pseudo MV-algebras, Discussiones Mathematicae - General Algebra and Applications 28 (2008), 63-75. Zbl1157.06006
- [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. Zbl0985.06007
- [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. Zbl1012.06012
- [11] J. Rachůnek, Prime spectra of non-commutative generalizations of MV-algebras, Algebra Univ. 48 (2002), 151-169. Zbl1058.06015
- [12] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287. Zbl1086.06011
- [13] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. Zbl0139.24606

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