Sources about transcendence degree

Question

I asked this question: Characterization of the transcendentals over a field

I realized I need some knowledge about transcendence degree to prove some facts in the book I'm reading.

I would like to know if someone can give some sources (PDF, books, sites, etc.) with some basic examples, theorems and known facts about transcendence degree. This would help me a lot.

Thanks in advance.

Answer 1

Any algebra book that treats field theory thoroughly should cover transcendental extensions and transcendence degree. I personally like the treatment of transcendence degree in Chapter VI, Section 1 of Hungerford's Algebra. There are probably lots of other good treatments, but that's the only algebra book with whose coverage of transcendence degree I'm familiar.