Sink Plumbing Doesn’t Vent to Roof?

I live in an apartment and my bathroom has two sinks. One of the sinks is completely missing the part of the plumbing that gets vented to the roof. This sink smells horrible due to lack of a vent. Maintenance thinks they can just put a cap on it to stop the sewage smell, but I’m concerned about pressure buildup. Anyone have any thoughts? Pics included to show where the plumbing stops.