A New Branch of the Pure Algebra: BCL-Algebras

Author(s)
Yonghong Liu

ABSTRACT

The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.

The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.

Cite this paper

nullY. Liu, "A New Branch of the Pure Algebra: BCL-Algebras,"*Advances in Pure Mathematics*, Vol. 1 No. 5, 2011, pp. 297-299. doi: 10.4236/apm.2011.15054.

nullY. Liu, "A New Branch of the Pure Algebra: BCL-Algebras,"

References

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[2] K. Iséki, “An Algebra Related with a Propositional Calculus,” Proceedings of the Japan Academy, Vol. 42, No. 1, 1966, pp. 26-29. doi:10.3792/pja/1195522171

[3] K. Iseki, “On BCI-Algebras,” Mathematics Seminar Notes (Kobe University), Vol. 8, No. 1, 1980, pp. 125-130.

[4] Q. P. Hu and X. Li, “On BCH-Algebras,” Mathematics Seminar Notes (Kobe University), Vol. 11, No. 2, 1983, pp. 313-320.

[5] Q. P. Hu and X. Li, “On Proper BCH-Algebras,” Mathematica Japonica, Vol. 30, No.4, 1985, pp. 659-661.

[6] Y. S. Huang, “BCI-Algebra,” Science Press, Beijing, 2006, p. 21.

[1] Y. Imai and K. Iséki, “On Axiom System of Propositional Cal-culi XIV,” Proceedings of the Japan Academy, Vol. 42, No. 1, 1966, pp. 19-22. doi:10.3792/pja/1195522169

[2] K. Iséki, “An Algebra Related with a Propositional Calculus,” Proceedings of the Japan Academy, Vol. 42, No. 1, 1966, pp. 26-29. doi:10.3792/pja/1195522171

[3] K. Iseki, “On BCI-Algebras,” Mathematics Seminar Notes (Kobe University), Vol. 8, No. 1, 1980, pp. 125-130.

[4] Q. P. Hu and X. Li, “On BCH-Algebras,” Mathematics Seminar Notes (Kobe University), Vol. 11, No. 2, 1983, pp. 313-320.

[5] Q. P. Hu and X. Li, “On Proper BCH-Algebras,” Mathematica Japonica, Vol. 30, No.4, 1985, pp. 659-661.

[6] Y. S. Huang, “BCI-Algebra,” Science Press, Beijing, 2006, p. 21.