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I often get confused when I want to distinguish the nouns as adjectives from possessive nouns.
For examples, these phrasings make me think and unsure.
Aren't we saying here that in 1. the syllabus has these highlights. 2. This relationship has these problems. 3. the admission has these requirments, which means they should be possessive nouns?
Please tell me how you have learned to distinguish between them easily.
We speak of possessive or genitive only when a noun (or noun phrase) is marked with the 's clitic (or with a bare apostrophe if the noun or noun phrase ends with ‹s› or ‹z›).
None of your examples employs this marker, so all of them are what grammarians call attributive nouns: nouns which act like adjectives 'modifying' a following noun.
(Some writers on grammar also call constructions with of preposition phrases, like NOUN of NOUN, 'genitive'; but that is not relevant here.)
The term possessive is a grammatical term, not a semantic one—that is, not a term which indicates actual "possession". There are other relationships which the possessive may signify. For instance, when the second noun, the one which is not possessive, is derived from a verb, the noun in the possessive case may be the agent, the semantic subject of the action which the second noun designates:
Columbus' discovery of America ← Columbus discovered America
In other cases the possessive may mark the patient, the semantic object of the action:
Germany's defeat by the Allies → Germany was defeated by the Allies
Attributive nouns have an even wider range of reference. A bicycle rider is someone who rides a bicycle, a bicycle store is a store where bicycles are sold, a bicycle tire is a tire for a bicycle, a bicycle race is a race in which the competitors ride bicycles. In your examples:
