Resumen de An elementary proof of a criterion for linear disjointness

David E. Dobbs

• An elementary proof using matrix theory is given for the following criterion: if F/Kand L/Kare field extensions, with Fand Lboth contained in a common extension field, then Fand Lare linearly disjoint over Kif (and only if) some K-vector space basis of Fis linearly independent over L. The material in this note could serve as enrichment material for the unit on fields in a first course on abstract algebra.