Kyungpook Mathematical Journal

  • 제64권2호
  • /
  • Pages.337-352
  • /
  • 2024
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

A Note on Theta Pairs for BCI-algebras

  • 투고 : 2023.09.12
  • 심사 : 2023.12.07
  • 발행 : 2024.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, first we show that all finite BCI-algebras are solvable. We then introduce the notion of a θ-pair for a maximal ideal of a BCI-algebra. Proving various properties of maximal θ-pairs, we use them to characterize solvable and nilpotent BCI-algebras.

키워드

참고문헌

  1. J. C. Beidleman, H. Smith, A note on supersoluble maximal subgroups and theta-pairs, Publ. Mat., 37(1)(1993), 91-94. https://doi.org/10.5565/PUBLMAT_37193_07
  2. S. A. Bhatti, M. A. Chaudhry, Ideals in BCI-algebras, Int. J. Math. Educ. Sci. Tech., 21(4)(1990), 637-643. https://doi.org/10.1080/0020739900210419
  3. X. Guo, On theta pairs for a maximal subgroup, Comm. Algebra., 22(1994), 4653-4659. https://doi.org/10.1080/00927879408825094
  4. W. Hung, Nil-radical in BCI-algebras, Math. Japon, 37(1992), 363-366.
  5. Y. Imai, K. Iseki, On axiom system of propositional calculi. XIV, Proc. Japan Academy, 42(1966), 19-22.
  6. K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy, 42(1966), 26-29. https://doi.org/10.3792/pja/1195522171
  7. S. Li, A note on theta pairs for maximal subgroups, Commun. Algebra., 26(1998), 4277-4284. https://doi.org/10.1080/00927879808826410
  8. E. Mohammadzadeh, R. A. Borzooei, Engel, nilpotent and solvable BCI-algebras, An. St. Univ. Ovidius Constanta, 27(1)(2019), 169-192. https://doi.org/10.2478/auom-2019-0009
  9. N. P. Mukherjee, P. Bhattacharya, On theta pairs for a maximal subgroup, Proc. Amer. Math. Soc., 109(1990), 585-596. https://doi.org/10.1090/S0002-9939-1990-1017843-X
  10. A. Najafi, A. Borumand Saeid, E. Eslami, Commutators in BCI-algebras, J. Intell. Fuzzy Syst., 31(1)(2016), 357-366. https://doi.org/10.3233/IFS-162148
  11. A. Najafi, A. Borumand Saeid, E. Eslami, Centralizers of BCI-algebras, Miskolc Math. Notes, 22(1)(2021), 407-425. https://doi.org/10.18514/MMN.2021.2632
  12. L. H. Shi, An axiom system of BCI-algebras, Math. Japon., 30(3)(1985), 351-352.
  13. H. Yisheng, BCI-Algebra, Science Press, Beijing, 2006.