teacher works at school, OR:at THE school

Thank you all for very many useful explanations.

Yet, I haven't got a clear answer if there is a rule for the use of zero article with 'school' if we speak of teachers, not pupils. In various forums they present either example as correct and common. So, do you know if there exists only one good rule for articles in front of 'place' nouns, if we speak of primary activities carried out in these places?

What is correct:

I work AT school (my activity is teaching pupils who are AT school). I am a teacher at school.

I work IN hospital (my activity is to give medication to patients, who are IN hospital). I am a doctor in hospital. I am a nurse in hospital.

Thank you!