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On ideals of BI-algebras. (English) Zbl 1460.06005

An AB-algebra \((X,\cdot,0)\) satisfying the identities \(xx=0\) and \(x\cdot yx=x\) is called a BI-algebra. Its nonempty subset \(N\) is normal if \(xa\cdot yb\in N\) for all \(xy,ab\in N\). A normal subset is a subalgebra, the relation \(x\sim y\) iff \(xy\in N\) is a congruence, and \(X/N\) is a BI-algebra. Elementary facts on homomorphisms of BI-algebras \(X\) and \(X?N\) are proved.

MSC:

06F35 BCK-algebras, BCI-algebras
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References:

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