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Haran's diamond theorem : ウィキペディア英語版 | Haran's diamond theorem In mathematics, the Haran diamond theorem gives a general sufficient condition for a separable extension of a Hilbertian field to be Hilbertian. == Statement of the diamond theorem ==
Let ''K'' be a Hilbertian field and ''L'' a separable extension of ''K''. Assume there exist two Galois extensions ''N'' and ''M'' of ''K'' such that ''L'' is contained in the compositum ''NM'', but is contained in neither ''N'' nor ''M''. Then ''L'' is Hilbertian. The name of the theorem comes from the pictured diagram of fields, and was coined by Jarden.
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