Could you put {ancient ziggurat} in a commander deck?
Yes, you can use {City of Brass}-type lands in EDH decks. They do not have a color identity. However, cards that produce any mana, yet also specifically produce green (or any color), have identity.
RESOLVED
So you could only add colors equal to your commanders identity to your mana pool with them?
Yes, otherwise they just produce colorless mana. To clarify though, {Watery Grave} can be used in a {Mirko Vosk, Mind Drinker} EDH, but {Steam Vents} cannot because of it's color identity of both {R} and {U}.
EDIT: Consider Coffee's explanation resolved.
So if I had {yeva, natures herald} as commander than {ancient ziggurat} would only produce green mana than. Or with krenko it would only produce red. Thank you
Correct.