Lattice of weak hyper K-ideals of a hyper K-algebra

Abstract

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a special subclass of this class togetherwith the suitable operations forms a Boolean lattice.

Keywords

• Hyper K-ideals
• weak hyper K-ideals
• Boolean lattice