"まま" means to continues to be/to let something remain in a particular position, place, or state, without changing, or to stay in a particular state/condition. I suppose yours is also fine, but buying can be ended without taking time. So I would say "本を買った が/けど、(まだ)読んでない (= I got a book, but I still haven't read it)" rather than "本を買ったまま読んでない."
扉が開いたままだ = The door has stayed/remained open or The door stayed/remained open.
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