Crossing cubic ideals of BCK/BCI-algebras

The notions of a crossing cubic ideal in a BCK/BCI-algebra, a closed crossing cubic ideal in a BCI-algebra, and a crossing cu-bic ◦-subalgebra of a BCK-algebra with the condition (S) are introduced, and several properties are investigated. The rela-tionship between them is established. Conditions for a crossing cubic structure to be a closed crossing cubic ideal are pro-vided. Conditions under which crossing cubic ideals are closed are explored. Characterizations of crossing cubic ideals are discussed. The translation of crossing cubic subalgebras and crossing cubic ideals are studied. Conditions for the translation of a crossing cubic structure to be a crossing cubic subalgebra (ideal) are provided, and its characterization is established.