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, Une famille z d'éléments de F qui est algébriquement indépendante sur E, et qui, en plus, est maximale (par rapport à l'inclusion (#7)), est appelée une base de transcendance de F/E. Le cardinal d'une telle famille z est appelé le degré de transcendance de F/E ; on le note deg tr F/E. (L'unicité du degré de transcendance d'une extension de corps de type finie suit de #11 et #10.) L'extension de corps F/E(z) est alors appelée algébrique
, E sont deux extensions de corps il en est de même pour