Distributive and Dual Distributive Elements in Hyperlattices

Abstract

In this paper we introduce and study distributive elements, dual distributive elements in hyperlattices, and prove that these elements forms ∧-semi lattice and ∨-semi hyperlattice, respectively. We use the properties of prime ideals and prime filters in hyperlattices. We will proceed to introduce the notion of dual distributive hyperlattices, I-filters and filters generated by dual distributive elements. Finally, the relationship between good homomorphisms and istributive (resp. dual distributive)elements in hyperlattices are investigated.

Keywords

• hyperlattice
• prime ideal
• prime filter
• distributive element
• dual distributive element
• homomorphism
• primary 15a24
• 15a60
• secondary 65f10