I'm renting a house that does not have a trap in the master bathroom. I've complained about the smell over and over to the property management but they still haven't done anything about it.
Is a trap required in every plumbing fixture? They keep blowing it off and I'd like to know.

YES! A trap porotects you from harmfull sewer gas. ( That's what you're smelling). This is a health hazard to you and your family. Call and report this to The Health Department as soon as possible. Also, you might check and see if you can get a rebate on your rent for having to live undere those conditions.
I bet that gets the attention of the
Property management. Good luck, n Tom