Loading... Prime filters of hyperlattices

What is it about?

The purpose of this paper is the study of prime ideals and prime filters in hyperlattices. I-filter and the filter generated by a in L are introduced. Moreover, we introduce dual distributive hyperlattices, and I filter in dual distributive hyperlattices. Some properties of hyperlattices are studied and the relationship between prime ideals and prime filters in hyperlattices is discussed.

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Why is it important?

The theory of hyperlattices was introduced by Konstantinidou in 1977. Rahnemaei Barghi considered the prime ideal theorem for distributive hyperlattices . B.B.N.Koguep, C. Nkuimi, and C. Lele studied ideals and filters in hyperlattices. Rasouli and Davvaz defined fundamental relation on a hyperlattice and obtained a lattice from a hyperlattice. Also, they defined a topology on the set of prime ideals of a distributive hyperlattice. In this paper, we introduce dual distributive hyperlattices, and I filter in dual distributive hyperlattices and study the properties. We consider relationship between prime ideals and prime filters in hyperlattices.