"The woman does not like the jacket."
Translation:Die Frau mag die Jacke nicht.
If you said "keine Jacke" it would be "No Jacket" or "She likes no jacket", which is different than "Sie mag die Jacke nicht" or "She likes the jacket not .". (Awkward English, but sometimes it helps to translate word-for-word)
She doesn't like any jacket vs She doesn't like the jacket.