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 $X$ with a constant $0$ and a binary operation $*$ satisfying the following axioms:
1) $x * x = 0$;
2) if $x * y = 0$ and $y * x = 0$, then $x = y$;
3) $(x*y)*z = (x*z)*y$.
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.
|[a1]||Qing-ping Hu, Xin Li, "On BCH-algebras" Math. Seminar Notes (Kobe University) , 11 (1983) pp. 313–320 Zbl 0579.03047|
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BCH-algebra. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=BCH-algebra&oldid=38750