The ring of trigonometric polynomials with complex scalars

Desvl at 
In this post we have investigated some basic facts of \(\mathbb{R}[\cos{x},\sin{x}]\) (henceforth notations used there will be here as well). It is a half factorial domain with ideal class group \(\mathbb{Z}/2\mathbb{Z}\), and hence not a UFD. Next, we jump to the complex scalar field, and there are……