In this manuscript at first by considering the notion of equivalence, regular and good, (ERG), relations on a hyper K-algebra H, we characterize it on a hyper Kalgebra H in which H is an (H-absorbing hyper K-ideal)-decomposable. Then we investigate the quotient hyper K-algebra related to an ERG relation on H. Moreover we show that the Theorem 4.1 and Corollary 4.3 of [2] are not true in general.