On embeddings of projective spaces - Taniguchi, Hiroaki (Utilitas Mathematica, 1998)
Let k, K be fields and n ≥ 3. Then an n-dimensional projective space Pn(k) can be embedded into a projective plane P2(K) if K is acyclic extension of k and dimk K ≥ n + 1. Conversely if an n-dimensional projective space Pn(k) is embedded into a projective plane P2 (K) then k is a subfield of K with dimk K ≥ n + 1.