Download PDF - On maximal ideals of pseudo-BCK-algebrasAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On maximal ideals of pseudo-BCK-algebras

Authors 1

Affiliations

  1. Institute of Mathematics and Physics, University of Podlasie, 3 Maja 54, 08-110 Siedlce, Poland

Abstract

We investigate maximal ideals of pseudo-BCK-algebras and give some characterizations of them.

Keywords

ENG
pseudo-BCK-algebra, (maximal) ideal

Bibliography

  1. C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490. doi: 10.1090/S0002-9947-1958-0094302-9
  2. G. Dymek and A. Walendziak, On maximal ideals of pseudo MV-algebras, Commentationes Mathematicae 42 (2007), 117-126.
  3. G. Dymek and A. Walendziak, Fuzzy ideals of pseudo-BCK-algebras, submitted.
  4. A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Dordrecht-Boston-London 2000.
  5. G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, p. 961-968 in: 'The Proc. of the Fourth International Symp. on Economic Informatics', Bucharest, Romania 1999.
  6. G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, p. 90-92 in: 'Abstracts of the Fifth International Conference FSTA 2000', Slovakia 2000.
  7. G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, p. 97-114 in: 'Proc. of DMTCS'01: Combinatorics, Computability and Logic', Springer, London 2001. doi: 10.1007/978-1-4471-0717-0_9
  8. G. Georgescu and A. Iorgulescu, Pseudo-MV algebras, Multiplae-Valued Logic 6 (2001), 95-135.
  9. P. Hájek, Metamathematics of fuzzy logic, Inst. of Comp. Science, Academy of Science of Czech Rep., Technical report 682 (1996).
  10. P. Hájek, Metamathematics of fuzzy logic, Kluwer Acad. Publ., Dordrecht, 1998.
  11. R. Halaš and J. Kühr, Deductive systems and annihilators of pseudo-BCK algebras, Ital. J. Pure Appl. Math., submitted.
  12. Y. Imai and K. Iséki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22. doi: 10.3792/pja/1195522169
  13. A. Iorgulescu, Classes of pseudo-BCK algebras, Part I, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 71-130.
  14. A. Iorgulescu, Classes of pseudo-BCK algebras, Part II, Journal of Multiplae-Valued Logic and Soft Computing 12 (2006), 575-629.
  15. A. Iorgulescu, Algebras of logic as BCK algebras, submitted.
  16. K. Isěki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japonicae 21 (1976), 351-366.
  17. Y.B. Jun, Characterizations of pseudo-BCK algebras, Scientiae Mathematicae Japonicae 57 (2003), 265-270.
  18. J. Kühr, Pseudo-BCK-algebras and related structures, Univerzita Palackého v Olomouci 2007.
  19. J. Kühr, Representable pseudo-BCK-algebras and integral residuated lattices, Journal of Algebra 317 (2007), 354-364. doi: 10.1016/j.jalgebra.2007.07.003
  20. J. Rachůnek, A non-commutative generalization of MV algebras, Czechoslovak Math. J. 52 (2002), 255-273.
Discussiones Mathematicae - General Algebra and Applications
2011/31/1
Export to PBN, Opens in new tab
Pages:
61-73
Main language of publication
English
Received
2010-03-08
Accepted
2010-06-14
Published
2011

DOI: 10.7151/dmgaa.1175

Exact and natural sciences