Talk:Adjunction (field theory)

Definition

I inserted some references, rewrote the definition of adjunction per the sources, and cited the sources. Both sources cited refer to a larger field E containing F and the generating set A but do not use the word "construction." I hope this is suitable.—Anita5192 (talk) 21:06, 25 November 2017 (UTC)

To editor Anita5192: As far as I know, adjunction is not a concept, but a term of jargon, which is typically used in sentences like: "the extension field obtained by adjoining a root of the polynomial p", "the splitting field of a polynomial p is obtained by adjoining all the root of p." This jargon is useful as it may be used without specifying how the field is constructed, which can be either as a subextension if one knows already a field containing the roots, or as $k[x]/p(x)$ for adjoining a root of an irreducible polynomial. Therefore I suggest to merge this article into Field extension#Extension field by adding there: An extension field of the form K(S) is often said resulting of the adjunction of S to K.

This page is not really used (empty talk page before your post, 10 views per day while there are almost 200 views per day for Field extension. Therefore, if you agree, we may be bold and do such a merge immediately. D.Lazard (talk) 10:44, 26 November 2017 (UTC)

I agree. I think the pages should be merged. I will leave the merging to you if you would like to do it.—Anita5192 (talk) 17:21, 26 November 2017 (UTC)

OK D.Lazard (talk) 17:22, 26 November 2017 (UTC)

 Done

To editor Anita5192: I have not merged the sources. Feel free do do that. D.Lazard (talk) 17:37, 26 November 2017 (UTC)