KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL

Abstract

Ternary semigroups 𝑇 is obtained from a nonempty set 𝑇 that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups 𝑇 is an ordered semigroup 𝑇 that satisfies the properties for each 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑇 if 𝑎 ≤ 𝑏 then (𝑎𝑐𝑑) ≤ (𝑏𝑐𝑑) and (𝑑𝑐𝑎) ≤ (𝑑𝑐𝑏). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroups. Furthermore, it will be discussed about the characteristics of minimal ordered left ideals on partially ordered semigroups.

Keywords : Ternary Semigroups, Ordered Ternary Semigroups, Left Ideals, Ordered Left Ideals, Minimal of Ordered Left Ideals.