On k-Subspaces of L-vector-spaces

Abstract

Let k ⊆ L be division rings, with [L: k]_right <∞ and let B_k ⊆ A_L be right vector spaces. Conditions are established in terms of the k-codimension of B in A, respectively the k-dimension of B, for there to exist a nonzero element a∈A such that aL∪B={0}, respectively an L-linear functional f on A such that f(B). Some consequences and related open questions are discussed.