On a vector space analogue of Kneser’s theorem

In a previous paper [X. Hou, K.H. Leung, Q. Xiang, A generalization of an addition theorem of Kneser, J. Number Theory 97 (2002) 1–9], the following result was established: let E⊂K be fields such that the algebraic closure of E in K is separable over E. Let A,B be E-subspaces of K such that 0