In this paper, we consider properties of weak extended order algebras with adjoint pairs and Galois pairs, and prove some new results. Moreover, we clarify the relation between these algebras and BCK-algebras, that is, the class of all normal weak extended order algebras with adjoint pair satisfying the condition x=x is identical the class of all BCK-algebras with the condition (S).
Michiro Kondo (Sat,) studied this question.
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