TY - JOUR ID - 784 TI - Ultra and Involution Ideals in $BCK$-algebras JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Saidi Goraghani, Simin AU - Borzooei, Rajab ali AD - Farhangian University AD - University of Beheshti Y1 - 2015 PY - 2015 VL - 2 IS - 2 SP - 23 EP - 36 KW - $BCK$-algebra KW - (associative KW - commutative KW - positive implicative KW - implicative) ideal KW - ultra ideal KW - involution ideal DO - N2 - 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. UR - https://as.yazd.ac.ir/article_784.html L1 - https://as.yazd.ac.ir/article_784_59ea8d93f1f07746b0ae002a32a6a389.pdf ER -