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On BN-algebras

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In this paper, we introduce a BN-algebra, and we prove that a BN-algebra is 0-commutative, and an algebra X is a BN-algebra if and only if it is a 0-commutative BF-algebra. And we introduce a quotient BN-algebra, and we investigate some relations between BN-algebras and several algebras.

Abstract

In this paper, we introduce a BN-algebra, and we prove that a BN-algebra is 0-commutative, and an algebra X is a BN-algebra if and only if it is a 0-commutative BF-algebra. And we introduce a quotient BN-algebra, and we investigate some relations between BN-algebras and several algebras.

참고문헌 (13)

  1. J. R. Cho, "On B-algebras and quasigroups", Quasigroups and related systems, 8, pp.1~6 (2001)
  2. Y. B. Jun, "On BH-algebra", Sci. Math., 1, pp.347~354 (1998)
  3. C. B. Kim, "On BG-algebras", Demo. Math., 41, pp.497~505 (2008)
  4. C. B. Kim, "On BM-algebras", Sci. Math. Japonicae, 63, pp.421~427 (2006)
  5. 김희식, "Coxeter algebras and pre-coxeter algebras in smarandache setting", 호남수학학술지, 26(4), pp.471~481 (2004), 호남수학회
  6. R. Mckenzie, "Algebras, Lattices, Varieties, Vol. 1", pp.1987, Wadsworth and Brooks
  7. J. Neggers, "On B-algebras", Mate. Vesnik, 54, pp.21~29 (2002)
  8. J. Neggers, "A fundamental theorem of B-homomorphism for B- algebras", Intern. Math. J., 2, pp.207~214 (2002)
  9. J. Neggers, "On -algebras", Math. Slovaca, 52, pp.517~530 (2002)
  10. A. Walendziak, "A note on normal subalgebras in B-algebras", Sci. Math. Japonicae, pp.49~53 (2005)
  11. A. Walendziak, "Some axiomatizations of B-algebras", Math Slovaca, 56, pp.301~306 (2006)
  12. A. Walendziak, "On BF-algebras", Math Slovaca, 57, pp.119~128 (2007)
  13. X. Zhang, "BZ-algebra and group", J. Math. Phy. Sci., 29, pp.223~233 (1995)

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