Modal operators on L-algebras

The main goal of this paper is to introduce analogously modal operators on L-algebras and study their properties. To begin with, we introduce the notion of modal operators on L-algebras and investigate some important properties of this operator. In order for the kernel of modal operator to be ideal, we investigate what conditions are required. Relations between modal operator and endomorphism of L-algebras are investigated. Also, we define the concept of positive L-algebra and some characterizations of positive L-algebra are established. Finally, we introduce a map k_{a} and show that k_{a} is a modal operator and we prove that the set of all k_{a} on a positive L-algebra makes a dual BCK-algebra.

Keywords:

BCK-algebra , L-algebra , Modal operator , Positive L-algebra