Talk:Field extension

Introduction does not define or describe field extension

but extension fields — Preceding unsigned comment added by 134.101.128.146 (talk) 15:21, 20 September 2018 (UTC)

Good point. Fixed. D.Lazard (talk) 16:51, 20 September 2018 (UTC)

"Purely transcendental extension" listed at Redirects for discussion

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"Trivial extension" listed at Redirects for discussion

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Are field extensions the only morphisms in the category of fields?

The "Caveats" section states: "Every ring homomorphism between fields is injective because fields do not possess nontrivial proper ideals, so field extensions are precisely the morphisms in the category of fields".

What about complex conjugation, isn't that a morphism of the field of complex numbers to itself? Is complex conjugation a field extension? Herpesklaus (talk) 19:11, 16 April 2026 (UTC)

complex conjugation is an isomorphism of fields. C \subseteq C is the trivial extension. there is no confusion and the clarification tag should be removed ~2026-33929-67 (talk) 08:17, 8 June 2026 (UTC)

The sentence is clearly wrong, since it can be only one field extension between two fields, and one may have several field homomorphisms between them. I tried to fix this, with examples. D.Lazard (talk) 14:58, 8 June 2026 (UTC)