Special types of NM-algebras

The main goal of this paper is to investigate (strong) NM-algebras and study some properties of them. Firstly, we define the notion of perfect NM-algebras and perfect filters on NM-algebras and give some theorems that characterize these algebraic structures. Therefore, the relations between proper NM-algebras and some filters, such as perfect filters and maximal filters have been established. Additionally, we introduce the notion of local NM-algebras and propose the theorems that characterize these algebraic structures.

Keywords:

NM-algebra , Filter , Perfect NM-algebra , Local NM-algebra