An elementary proof of a criterion for linear disjointness

• Autores: David E. Dobbs
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 4, 2013, págs. 614-617
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.742155
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• Resumen

  • 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.