A-ideals and fuzzy A-ideals of ternary semigroups

Abstract

A ternary semigroup is a nonempty set together with a ternary multiplication that is associative. Every semigroup can be reduced to a ternary semigroup, but a ternary semigroup does not necessarily reduce to a semigroup. The notion of A-ideals in semigroups was introduced by Grosek and Satko in 1980. Fuzzy sets were introduced by Zadeh in 1965. Applications of the fuzzy set theory have been found in various fields. The theory of fuzzy sets has been studied in various kinds of algebraic systems. In this paper, we define and study some properties of A-ideals and fuzzy A-ideals of ternary semigroups. Moreover, we introduce the notion of minimal fuzzy A-ideals of ternary semigroups and study properties of them.

Keywords

• A-ideals
• fuzzy A-ideals
• minimal A-ideals
• ternary semigroups