Talk:Transcendental extension

It wpuld be nice to have a comment on the relation between transcendence degree and vector space dimension

"Exchange lemma"

"The proof that any two bases have the same cardinality depends, in each setting, on an exchange lemma." What is an "exchange lemma"? I'm unable to find other uses of this phrase - nonstandard terminology, perhaps? —The preceding unsigned comment was added by 70.48.179.234 (talk) 14:23, 13 May 2007 (UTC). - I suppose it is a (incorrect?) translation of the German "Austauschlemma" ("Given a basis and an element v (not 0) of a vector space, one can exchange one of the basis elements by v to get a new basis" -- see de:Basis (Vektorraum)). But I don't know of a corresponding theorem for the transcendence degree.--129.70.15.202 (talk) 19:33, 18 May 2008 (UTC)[reply]

Merge trdeg into this article

Trdeg is a short, new article that defines the notation trdeg and states a theorem relating the geometric idea of transcendence degree with the algebraic one. I don't think this is specifically in this article already, but the last paragraph is certainly along the same lines. Trdeg is just a stub and needs language cleanup and references; I think this article could use a reference but most abstract algebra texts should work. JackSchmidt (talk) 14:30, 21 November 2007 (UTC)[reply]