Corollary

Let K be a commutative field and M a vector space over K. For every element $z \in S(M)$ there exists a smallest vector space N of M such that $z \in S(N)$ and N is finite-dimensional.

The proof is derived from that of § 5, no. 2, Corollary to Proposition 4 replacing T by S throughout.

N is called the vector subspace of M associated with z.