DOI QR코드

DOI QR Code

On the Construction of Polynomial β-algebras over a Field

  • 투고 : 2016.09.22
  • 심사 : 2016.11.10
  • 발행 : 2017.03.23

초록

In this paper we construct quadratic ${\beta}-algebras$ on a field, and we discuss both linear-quadratic ${\beta}-algebras$ and quadratic-linear ${\beta}-algebras$ in a field. Moreover, we discuss some relations of binary operations in ${\beta}-algebras$.

키워드

참고문헌

  1. P. J. Allen, H. S. Kim and J. Neggers, B-algebras and groups, Sci. Math. Japo., 9(2003), 9-17.
  2. A. Iorgulescu, Algebras of logic as BCK-algebras, Editura ASE, Bucharest, 2008.
  3. K. Iseki, On BCI-algebras, Math. Seminar Notes, 8(1980), 125-130.
  4. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica, 23(1978), 1-26.
  5. H. S. Kim and H. G. Park, On 0-commutative B-algebras, Sci. Math. Japo., 62(2005), 7-12.
  6. Y. H. Kim and K. S. So, $\beta$-algebras and related topics, Comm. Korean Math. Soc., 27(2012), 217-222. https://doi.org/10.4134/CKMS.2012.27.2.217
  7. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa, Seoul, 1994.
  8. J. Neggers and H. S. Kim, On B-algebras, Mat. Vesnik, 54(2002), 21-29.
  9. J. Neggers and H. S. Kim, On $\beta$-algebras, Mat. Slovaca, 52(2002), 517-530.
  10. H. Yisheng, BCI-algebras, Science Press, Beijing, 2006.