What is the ruling on Friday prayer for a traveler who works in the desert for a month?

If the desert is far from the place where Jumu'ah prayer is established and there are no settlers there upon whom Jumu'ah is obligatory, then your prayer is Dhuhr. However, if it is close enough that you can hear the Adhan, or if there are settlers with you upon whom Jumu'ah is obligatory, then Jumu'ah prayer becomes obligatory upon you.