Noetherian and Artinian pseudo MV-algebras

Grzegorz Dymek

Discussiones Mathematicae - General Algebra and Applications (2008)

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

Abstract

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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.

How to cite

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Grzegorz 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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  1. [1] C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. Zbl0084.00704
  2. [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
  3. [3] A. Dvurečenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327. Zbl0999.06011
  4. [4] G. Dymek, Fuzzy maximal ideals of pseudo MV-algebras, Comment. Math. 47 (2007), 31-46. Zbl1177.06015
  5. [5] G. Dymek, Fuzzy prime ideals of pseudo MV-algebras, Soft Computing 12 (2008), 365-372. Zbl1132.06006
  6. [6] G. Dymek, On fuzzy ideals of pseudo MV-algebras, Discussiones Mathematicae - General Algebra and Applications 28 (2008), 63-75. Zbl1157.06006
  7. [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. [8] G. Georgescu and A. Iorgulescu, Pseudo MV-algebras, Multi. Val. Logic 6 (2001), 95-135. 
  9. [9] Y.B. Jun and A. Walendziak, Fuzzy ideals of pseudo MV-algebras, Inter. Review. Fuzzy Math. 1 (2006), 21-31. 
  10. [10] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. Zbl1012.06012
  11. [11] J. Rachůnek, Prime spectra of non-commutative generalizations of MV-algebras, Algebra Univ. 48 (2002), 151-169. Zbl1058.06015
  12. [12] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287. Zbl1086.06011
  13. [13] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. Zbl0139.24606

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