ON BP-ALGEBRAS

Year 2013, Volume: 42 Issue: 5, 551 - 557, 01.05.2013

Sun Shin Ahn Jeong Soon Han

Abstract

In this paper, we introduce the notion of a BP -algebra, and discusssome relations with several algebras. Moreover, we discuss a quadraticBP -algebra and show that the quadratic BP -algebra is equivalent toseveral quadratic algebras.

Keywords

B-algebra, 0-commutative, BF -algebra, BP -algebra, BH-algebra, (normal) subalgebra.

References

• Q. P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983), 313-320.
• Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japo. 30 (1985), 659-661.
• K. Is´ eki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125-130.
• K. Is´ eki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japo. 23 (1978), 1Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math. 1(1998), 347–354.
• C. B. Kim and H. S. Kim, On BG-algebras, Mate. Vesnik 41 (2008), 497-505.
• H. S. Kim and N. R. Kye, On quadratic BF -algebras, Sci. Math. Jpn. 65, 287-290. H. S. Kim and H. D. Lee, A quadratic BG-algebras, Int. Math. J. 5 (2004), 529-535.
• H. S. Kim and H. G. Park, On 0-commutative B-algebras, Sci. Math. Jpn. 62(2005), 7–12. J. Neggers, S. S. Ahn and H. S. Kim, On Q-algebras, Int. J. Math. & Math. Sci. 27 (2001), 749-75
• J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), 19-26.
• J. Neggers and H. S. Kim, On B-algebras, Math. Vesnik 54 (2002), 21-29.
• H. K. Park and H. S. Kim, On quadratic B-algebras, Quasigroups and Related Sys., 7(2001), 67-7
• A. Walendiziak, Some axiomatizations of B-algebras, Math. Slovaca, 56 (2006), 301–306. A. Walendiziak, On BF -algebras, Math. Slovaca, 57 (2007), 119–128.