Communications of the
Korean Mathematical Society CKMS

In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of ``$c_f\text{-Max}~X$", we prove that every member of ``$c_f\text{-Max}~X$" is a prime ideal. Also we conclude some more related results.

Keywords: BCI-algebra, BCK-algebra, closure operation, finite type closure operation, semi-prime closure operation

MSC numbers: Primary 06F35, 03G25