Linear subspace of polynomial ring

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There should be a way, since the category framework knows that R is a vector space:

sage: R.categories()
[Join of Category of unique factorization domains and Category of commutative algebras over Rational Field,
 Category of unique factorization domains,
 Category of gcd domains,
 Category of integral domains,
 Category of domains,
 Category of commutative algebras over Rational Field,
 Category of algebras over Rational Field,
 Category of commutative rings,
 Category of rings,
 Category of rngs,
 Category of semirings,
 Category of monoids,
 Category of semigroups,
 Category of magmas,
 Category of vector spaces over Rational Field,
 Category of modules over Rational Field,
 Category of bimodules over Rational Field on the left and Rational Field on the right,
 Category of right modules over Rational Field,
 Category of left modules over Rational Field,
 Category of commutative additive groups,
 Category of commutative additive monoids,
 Category of commutative additive semigroups,
 Category of additive magmas,
 Category of sets,
 Category of sets with partial maps,
 Category of objects]

sage: R in VectorSpaces(QQ)
True

But then, i do not know what explicit things i can do with that... It could be nice to inherits all features of a vector space. I will ping specialists to explain what can be done.