The article introduces new concepts in a type of mathematical structure called po ternary semigroups. It shows that certain elements in these structures have special properties, and if an element is completely regular, it is also left, lateral, and right regular. The study proves that in po ternary semigroups, if principal po ideals form a chain, then all po ideals also form a chain. It also establishes that a po ternary semigroup is simple if and only if a specific equation holds true for all elements in the structure.