Octahedron $KU$-ideals of $KU$-algebras

Abstract

In this paper, we introduce the notion of octahedron $KU$-subalgebras and octahedron $KU$-ideals of a $KU$-algebra, and study there properties. Also, we define a level set of an octahedron set and deal with relationships between octahedron $KU$-subalgebras [resp. octahedron $KU$-ideals] and $KU$-subalebras [resp. $KU$-ideals] of a $KU$-algebra. Next, we discuss some properties of the image [resp. preimage] of octahedron $KU$-ideals under a $KU$-homomorphism. Finally, the Cartesian product of two octahedron $KU$-ideals of the Cartesian product of two $KU$-algebras is studied.