DOI QR코드

DOI QR Code

ON AMR-ALGEBRA

  • AMIN, AMR K. (Department of Basic Sciences, Adham University College, Umm AL-Qura University, Department of Mathematics and computer Science, Faculty of Science, Beni-Suef University)
  • 투고 : 2022.01.08
  • 심사 : 2022.08.09
  • 발행 : 2022.09.30

초록

The main objective of this paper is to introduce the notion of AMR-algebra and its generalization, and to compare them with other algebras such as BCK, BCI, BCH, · · ·, etc. We show moreover that the K-part of AMR-algebra is an abelian group, and the weak AMR-algebra is also an abelian group and generalizes many known algebras like BCI, BCH, and G.

키워드

과제정보

The author would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (43405002) (22UQU4331287DSR04).

참고문헌

  1. Q.P. Hu and X. Li, On BCH-algebras, Mathematics Seminar Notes 11 (1983), 313-320.
  2. Y. Imai and K. Iseki, On axiom systems of propositional calculi, Proc. Japan acad. 42 (1996), 19-22. https://doi.org/10.3792/pja/1195522169
  3. Y.B. Jun, E.H. Roh, and H.S. Kim, On BH-algebras, Sci. Math. Japonica 1 (1998), 347-354.
  4. C.B. Kim and H.S. Kim, On BM-algebras, Sci. Math. Japonicae 63 (2006), 421-427.
  5. C.B. Kim and H.S. Kim, On BG-algebras, Demonstr. Math. 41 (2008), 497-505. https://doi.org/10.1515/dema-2008-0303
  6. Y.L. Liu, Y. Xu and J. Meng, BCI-implicative ideals of BCI-algebras, Inform. Sci. 177 (2007), 4987-4996. https://doi.org/10.1016/j.ins.2007.07.003
  7. J. Neggers, S.S. Ahn, and H.S. Kim, On Q-algebras, Int. J. Math. and Math. Sci. 27 (2001), 749-757. https://doi.org/10.1155/S0161171201006627
  8. J. Neggers and H.S. Kim, On B-algebras, Math. Vensik 54 (2002), 21-29.
  9. R.A.K. Omar, On RG-algebras, Pure Math. Sci. 3 (2014), 59-70. https://doi.org/10.12988/pms.2014.31119
  10. A. Walendziak, On BF-algebras, Math. Slovaca 57 (2007), 119-128. https://doi.org/10.2478/s12175-007-0003-x
  11. M. Chandramouleeswaran, P. Muralikrishna, K. Sujatha and S. Sabarinathan, A note on Z-algebra, Ital J. Pure Appl. Math. 38 (2017), 707-714.
  12. Ravi Kumar Bandru, On BRK-algebras, International Journal of Mathematics and Mathematical Sciences 2012 (2012), 1-12. https://doi.org/10.1155/2012/952654
  13. M. Kondo, On the class of QS-algebras, Int. J. Math. and Math. Sc. 2004 (2004), 2629-2639. https://doi.org/10.1155/S0161171204309154
  14. C.B. Kim and H.S. Kim, On BO-algebras, Math. Slovaca 62 (2012), 855-864. https://doi.org/10.2478/s12175-012-0050-9