If $E_1,E_2$ are intermediate fields, then
(i) tr.d.$E_1E_2/K \ge$ tr.d.$E_i/K$ for $i= 1,2$;
(ii) tr.d.$E_1E_2/K \le$ (tr.d.$E_1/ K$) + (tr.d.$E_2/ K$).
tr.d. denotes the transcendence degree.
2026-05-13 18:29:13.1778696953
Transcendence degree of product of intermediate fields
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