"The woman does not have a buyer."
Translation:Die Frau hat keinen Käufer.
I'm not entirely sure what the difference between those two sentences are. If I were to hazard a guess, I'd say that the first one implies that the woman doesn't have a buyer (in this particular case) whereas the second one may imply that she perpetually doesn't have a buyer. That's only my guess though. As far as I'm aware, if you're talking about having zero of some noun then you should use 'kein', whereas for negating an action or a predicate requires 'nicht'.
ohh If I understand you correctly... You can tell it's singular because 'keinen' is for masculine, singular nouns in the accusative case. Plural nouns in the accusative case would use 'keine'. You can always think of kein(e/en/em/er/es) as the negative indefinite article; that is, 'not ... a'. The woman does <sub>not</sub> have <sub>a</sub> buyer. Does that help?