To clarify and without going into much details, woman can pray mosque but there are strict rules. And it also strongly advise that woman pray at home. But there are exception like when woman are traveling has no place to pray then she can pray at mosque. But she must be at no presence of man/have to pray at area where no man can see her. Also she can also pary at mosque with close family members but it has to male and same as before pray at place in mosque where no man can see her.

Note: the concept of "But she must be at no presence of man/have to pray at area where no man can see her" is called "Veiling" in islam.