# 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……