Simin Saidi Goraghani - Farhangian University
Rajab ali Borzooei - University of Beheshti

In this paper, we define the notions of ultra and involution ideals in BCK-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative BCK-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower BCK-semilattice, the notions of prime ideals and ultra ideals are coincide.

BCK-algebra, (associative, commutative, positive implicative, implicative) ideal, ultra ideal, involution ideal