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On $$d$$-ideals in $$d$$-algebras. (English) Zbl 0960.06010
Motivated by the theory of BCK-algebras, the authors introduce the notions of $$d$$-subalgebras and $$d$$-ideals on $$d$$-algebras. A $$d$$-algebra is an algebra $$(X;\ast ,0)$$ of type $$(2,0)$$ such that (i) $$x \ast x = 0$$, (ii) $$0 \ast x = 0$$, and (iii) $$x \ast y = 0$$ and $$y \ast x = 0$$ imply $$x = y.$$ The idea of a quotient $$d$$-algebra is introduced, some fundamental theorems of $$d$$-morphisms for $$d$$-algebras are presented, and some relationships among different types of $$d$$-ideals are given.

##### MSC:
 06F35 BCK-algebras, BCI-algebras
##### Keywords:
BCK-algebra; $$d$$-algebras; $$d$$-subalgebra; $$d$$-ideals
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##### References:
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