Talk:Construction of splitting fields

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  • may be something useful there, but its not accessible for the general user in the form it is now. also probably too detailed. Also likely a straight copy of a text. Bwithh 06:51, 17 October 2005 (UTC)

I rewrote the page and fixed some of the inaccuracies. At some point I hope to add some more examples. TooMuchMath 11:48, 6 February 2006 (UTC)

Quotient or extension[edit]

Can someone have a look at where this article refers to quotient ring and see if this should be field extension instead? It looks like the two concepts are different but have similar notation, e.g. see field extension. I thought the quotient ring was *smaller* than what you started with but the field extension should be in some sense bigger. I changed the article (wasn't logged on) but then changed it back as I was not sure. Danpovey (talk) 00:54, 15 February 2010 (UTC)

The quotient K[x]/(f(x)) would be a field extension if f were irreducible over K. With infinite sets there is no bigger or smaller. If you are talking about inclusion, then K[x] or the rational field extension K(x) contain K, as does K[x]/(f(x)), but the latter is in some sense smaller than K[x], since its elements are equivalence classes, which are subsets of K[x].--LutzL (talk) 10:04, 15 February 2010 (UTC)
On second view, in the previous step f is chosen as an irreducible factor, so that field extension would be correct. And the desired end result is a finitely generated field extension, constructed as a chain of field extensions, so that it should be mentioned in the iteration step.--LutzL (talk) 10:07, 15 February 2010 (UTC)

Could someone also prove uniqueness up to isomorphism? I think that would be a nice addition to the article.

Thanks, Maks. —Preceding unsigned comment added by (talk) 07:11, 22 August 2010 (UTC)