My answer was going to be the same as Maria's, so now I'm confused.

However, I do know of a really easy and boring way to make the complex numbers, \\(\mathbb{C}\\), into a commutative monoidal poset with the usual \\(+\\) and \\(0\\) and some concept of \\(\le\\).

Take the zero function,

$$

F(z) = 0*z

$$

then all the required axioms will hold trivially.

However, I do know of a really easy and boring way to make the complex numbers, \\(\mathbb{C}\\), into a commutative monoidal poset with the usual \\(+\\) and \\(0\\) and some concept of \\(\le\\).

Take the zero function,

$$

F(z) = 0*z

$$

then all the required axioms will hold trivially.