Kyungpook Mathematical Journal

  • 제55권4호
  • /
  • Pages.859-870
  • /
  • 2015
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Quasi-Valuation Maps on BCK/BCI-Algebras

  • SONG, SEOK-ZUN (Department of Mathematics, Jeju National University) ;
  • ROH, EUN HWAN (Department of Mathematics Education, Chinju National University of Education) ;
  • JUN, YOUNG BAE (Department of Mathematics Education, Gyeongsang National University)
  • 투고 : 2014.05.30
  • 심사 : 2015.12.02
  • 발행 : 2015.12.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

키워드

참고문헌

  1. Y. S. Huang, BCI-algebra, Science Press, China (2006).
  2. Y. Imai and K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42(1966), 19-22.
  3. K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42(1966), 26-29. https://doi.org/10.3792/pja/1195522171
  4. K. Iseki, On BCI-algebras, Math. Seminar Notes, 8(1980), 125-130.
  5. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica, 23(1978), 1-26.
  6. J. Meng, Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul (1994).
  7. J. Neggers, A. Dvurecenskij and H. S. Kim, On d-fuzzy functions in d-algebras, Found. Phys., 30(2000), 1807-1816. https://doi.org/10.1023/A:1026466720971
  8. J. Neggers, Y. B. Jun, H. S. Kim, On d-ideals in d-algebras, Math. Slovaca, 49(1999), 243-251.
  9. J. Neggers, H. S. Kim, On d-algebras, Math. Slovaca, 49(1999), 19-26.
  10. L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci., 172(2005), 1-40. https://doi.org/10.1016/j.ins.2005.01.017

피인용 문헌

  1. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps vol.7, pp.2, 2018, https://doi.org/10.3390/axioms7020026