Let $R$ be an integral domain over a field $k$. Is it true, that $\deg.\mathrm{tr}_k \ \mathrm{Frac}(R)$ is the greatest number of elements of $R$ algebraically independent over $k$?
Transcendence degree for a $k$-algebra which is an integral domain
3
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abstract-algebra
commutative-algebra
field-theory
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3Yes: http://mathoverflow.net/questions/75219 – 2012-10-28