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On BH-algebras. (English) Zbl 0928.06013
Summary: We introduce a new notion, BH-algebra, which is a generalization of BCH/BCI/BCK-algebras. We define the notions of ideals and boundedness in BH-algebras, and show that there is a maximal ideal in bounded BH-algebras. Furthermore, we construct the quotient BH-algebras via translation ideals and obtain the fundamental theorem of homomorphisms for BH-algebras as a consequence.

##### MSC:
 06F35 BCK-algebras, BCI-algebras
##### Keywords:
BH-algebra; ideals; boundedness; quotient; homomorphisms