LATTICE OF WEAK HYPER K-IDEALS OF A HYPER K-ALGEBRA

In this note, we study the lattice structure of the class of all weak hyper K-ideals of a hyper K-algebra. We rst introduce the notion of (left, right) scalar element in a hyper K-algebra which helps 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 a hyper K-algebra and prove that, under suitable conditions, a special subclass of this class forms a Boolean lattice.