Is there a better way to name this? It seems crappy to me but it's all I got. --Grambottle 14:53, 19 December 2008 (UTC)

"Field Adjoined with Element" would suit the general style that we've developed up till now.

Something else you might want to consider:

a) We've been using a system whereby the major words in a definition or proof are capitalised as I've just done. I think there was something said some time ago about this being the house style.

b) When I've put pages together I've tried to make sure that any page can be interpreted without any prior knowledge. So anything used in a page that is jargon in any way is provided with a link to a page where that element is defined (and elements in that page are also defined, and so on back to the first-principle definitions). E.g. in this page there's "field extension" and $F[\alpha]$ and $F(\alpha)$ and so on.

This is only a suggestion - if you think that anyone looking at this site ought to be sufficiently mathematically literate that they ought to know what these things mean, then fair enough - after all, it takes a fair amount of work to find the references elsewhere in proofwiki which you may not have the time or inclination or patience to hunt down.

But I'm not the guru, I'm just an amateur out of touch with current mathematical development and attitudes so I'm probably way off beam.--prime mover (talk) 07:20, 20 December 2008 (UTC)

I'm happy with this proposed move. If anyone else is, let's go for it. Remind me to do it if I forget, or another admin bod can. --prime mover 02:56, 30 May 2011 (CDT)

They are Definition:Generated Algebra over Ring and Definition:Generated Field Extension, not generated field. --barto (talk) (contribs) 16:06, 14 January 2018 (EST)