In this paper, we are going to introduce a fundamental relation "delta" on (hyper BE-algebra) dual hyper K-algebra and investigate some properties. We show that quotient of any dual hyper K-algebra via a regular relation is a hyper BE-algebra and this quotient, via any strongly regular relation is a BE-algebra. Furthermore, it shows that "delta" under some condition is transitive and quotient of any weak commutative dual hyper K-algebra via "delta*" is a dual BCK-algebra.
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