transcendence degree

Noun

transcendence degree (plural transcendence degrees)

1. (field theory) Given a field extension L / K, the largest cardinality of an algebraically independent subset of L over K.
   • Let F_1/k and F_2/k denote algebraic function fields of transcendence degree one.2004, F. Hess, An Algorithm for Computing Isomorphisms of Algebraic Function Fields, Duncan Buell (editor), Algorithmic Number Theory: 6th International Symposium, ANTS-VI, LNCS 3076, page 263
   • Lemma 7.19 Suppose that L is a field extension^([sic – meaning extension field]) of transcendence degree r over a field K and that L is not separably generated over K. If x#95;1,#92;dots,x#95;n are elements of L such that L#61;K(x#95;1,#92;dots,x#95;n), then for a suitable relabeling of the...2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 422

   Synonyms:

   transcendental degree