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BCH-algebra

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A variant of a BCI-algebra. One can define it by taking some of the axioms for a BCI-algebra and some of the important properties of a BCI-algebra. Specifically, a BCH-algebra is a non-empty set with a constant and a binary relation satisfying the following axioms:

1) ;

2) if and , then ;

3) . Clearly a BCI-algebra is a BCH-algebra; however, the converse is not true. While some work has been done on such algebras, generally they have not been as extensively investigated as BCI-algebras.

References

[a1] Qing-ping Hu, Xin Li, "On BCH-algebras" Math. Seminar Notes (Kobe University) , 11 (1983) pp. 313–320
[a2] Y. Imai, K. Iséki, "On axiom systems of propositional calculi, XIV" Proc. Japan Acad. Ser. A Math. Sci. , 42 (1966) pp. 19–22
[a3] K. Iséki, "An algebra related with a propositional calculus" Proc. Japan Acad. Ser. A, Math. Sci. , 42 (1966) pp. 26–29
How to Cite This Entry:
BCH-algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=BCH-algebra&oldid=17336
This article was adapted from an original article by C.S. Hoo (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article