Commutative falling neutrosophic ideals in BCK-algebras

Abstract

The notions of a commutative (is an element of, is an element of)-neutrosophic ideal and a commutative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a commutative (is an element of, is an element of)-neutrosophic ideal are obtained. Relations between commutative (is an element of, is an element of)-neutrosophic ideal and (is an element of, is an element of)-neutrosophic ideal are discussed. Conditions for an (is an element of, is an element of)-neutrosophic ideal to be a commutative (is an element of, is an element of)-neutrosophic ideal are established. Relations between commutative (is an element of, is an element of)-neutrosophic ideal, falling neutrosophic ideal and commutative falling neutrosophic ideal are considered. Conditions for a falling neutrosophic ideal to be commutative are provided.