본문 바로가기
KERD
논문KCI 등재

Fuzzy Prime Ideals of Pseudo- LBCK-algebras

Grzegorz Dymek|Andrzej Walendziak
경북대학교 자연과학대학 수학과|2015.03|Kyungpook Mathematical Journal|제55권 제1호|pp. 51-62|DOI http://dx.doi.org/10.5666/KMJ.2015.55.1.51

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

(fuzzy) idealPseudo-BCK-algebrapseudo- LBCK-algebra(fuzzy) prime ideal
주제분류수학

초록

Pseudo- LBCK-algebras are commutative pseudo-BCK-algebras with relativecancellation property. In the paper, we introduce fuzzy prime ideals in pseudo- LBCKalgebrasand investigate some of their properties. We also give various characterizations ofprime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo- LBCKalgebrato be a pseudo- LBCK-chain.

Abstract

Pseudo- LBCK-algebras are commutative pseudo-BCK-algebras with relativecancellation property. In the paper, we introduce fuzzy prime ideals in pseudo- LBCKalgebrasand investigate some of their properties. We also give various characterizations ofprime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo- LBCKalgebrato be a pseudo- LBCK-chain.

참고문헌 (23)

  1. C. C. Chang, "Algebraic analysis of many valued logics", Trans. Amer. Math. Soc, 88, pp.467~490 (1958)
  2. G. Dymek., "Fuzzy ideals of pseudo-BCK-algebras", Demonstratio Mathematica, 45, pp.1~15 (2012)
  3. A. Dvurecenskij., "Algebras in the positive cone of po-groups", Order, 19, pp.127~146 (2002)
  4. G. Georgescu, "Pseudo-MV algebras: a noncommutative extension of MV algebras", In: The Proc. of the Fourth International Symp. on Economic Informatics, Bucharest, Romania, pp.961~968 (1999)
  5. G. Georgescu, "Pseudo-BL algebras: a noncommutative extension of BL algebras", In: Abstracts of the Fifth International Conference FSTA 2000, Slovakia, pp.90~92 (2000)
  6. G. Georgescu, "Pseudo-BCK algebras: an extension of BCK alge- bras", In: Proc. of DMTCS'01: Combinatorics, Computability and Logic, pp.97~114 (2001), Springer
  7. G. Georgescu., "Pseudo-MV algebras", Multiplae-Valued Logic, 6, pp.95~35 (2001)
  8. Metamathematics of fuzzy logic, "P. Hajek", Inst. of Comp. Science, Academy of Science of Czech Rep., ~, pp.Technical report 682 (1996)
  9. P. Hajek, "Metamathematics of fuzzy logic" (1998), Kluwer Acad. Publ.
  10. R. Halas., "Deductive systems and annihilators of pseudo-BCK algebras", Italian Journal of Pure and Applied Mathematics, 25, pp.83~94 (2009)
  11. W. Huang., "Ideals and subalgebras in BCI algebras", South. Asian Bull. Math, 26, pp.567~573 (2002)
  12. Y. Imai., "On axiom systems of propositional calculi XIV", Proc. Japan Academy, 42, pp.19~22 (1966)
  13. A. Iorgulescu., "Classes of pseudo-BCK algebras, Part I", Journal of Multiplae-Valued Logic and Soft Computing, 12, pp.71~130 (2006)
  14. A. Iorgulescu., "Classes of pseudo-BCK algebras, Part II", Journal of Multiplae-Valued Logic and Soft Computing, 12, pp.575~629 (2006)
  15. Y. B. Jun, "Characterizations of pseudo-BCK algebras", Scientiae Mathematicae Japonicae, 57, pp.265~270 (2003)
  16. J. Kuhr, "Pseudo BCK-semilattices", Demonstratio Mathematica, 40, pp.495~516 (2007)
  17. J. Kuhr, "Pseudo-BCK-algebras and related structures", pp.2007
  18. J. Kuhr, "Commutative pseudo-BCK-algebras", Southeast Asian Bulletin of Mathematics, 33, pp.463~486 (2009)
  19. J. Rachunek, "A non-commutative generalization of MV algebras", Czechoslovak Math. J, 52, pp.255~273 (2002)
  20. A. Walendziak, "On axiom systems of pseudo-BCK-algebras", Bulletin of the Malaysian Mathematical Sciences Society, 34, pp.287~293 (2011)
  21. A. Walendziak., "On maximal ideals of pseudo-BCK-algebras, Discussiones Mathematicae", General Algebra and Applications, 31, pp.61~73 (2011)
  22. O. G. Xi, "Fuzzy BCK-algebras", Math. Japon, 36, pp.935~942 (1991)
  23. L. A. Zadeh, "Fuzzy sets", Inform. Control, 8, pp.338~353 (1965)

관련 논문AI추천

Fuzzy Ideals in Γ-BCK-AlgebrasArsham Borumand Saeid, M. Murali Krishna Rao, Rajendra Kumar Kona한국수학교육학회 · 이론수학과 교직수학2023 · 제30권 제4호SOME RESULTS ON FUZZY IDEAL EXTENSIONS OF BCK-ALGEBRAS정원균영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호Positive implicative vague ideals in BCK-algebrasKyoung Ja Lee, Young Bae Jun기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2011 · 제1권 제1호Vague BCK/BCI-algebras방금성, 소금숙, 이경자한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제3호Subalgebras and Ideals of BCK/BCI-Algebras in the Framework of the Hesitant IntersectionYOUNG BAE JUN경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호ANTI FUZZY IDEALS IN WEAK BCC-ALGEBRASBushra Karamdin영남수학회 · East Asian Mathematical Journal2010 · 제26권 제3호

이 간행물의 다른 논문 (21건)

On Skew Centralizing Traces of Permuting n-Additive MappingsNazia Parveen, Mohammad Ashrafpp. 1-12Distributivity on the Gyrovector Spaces김세정pp. 13-20A Note on Skew-commuting Automorphisms in Prime RingsTarannum Bano, Nadeem Ur Rehmanpp. 21-28Functional Equations associated with Generalized Bernoulli Numbers and Polynomials장유선, 유천성, 권혁인, Dmitry Victorovich Dolgypp. 29-39Some Additive Maps on Sigma Prime RingsMohammad Mueenul Hasnain, Mohd Rais Khanpp. 41-50
원문 보기