Talk:Separable extension

message: shouldn't it be said anything about non-algebraic separable extensions?
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and we seem to be missing any mention of separability degree... Dmharvey 00:40, 18 April 2006 (UTC)
thread_title:  Suggestions 

message: A concrete example of one of these would be pretty cool to have in the article... -140.105.47.84 (talk) 07:24, 17 September 2009 (UTC)
replies: text: Well, there is one (function fields). To specialise, take K(T), rational functions in T where K has characteristic p. This is purely inseparable over its subfield K(Tp). Which is isomorphic as field ... so the rational function field is not perfect. Charles Matthews (talk) 11:15, 17 September 2009 (UTC)
thread_title:  Example of non-perfect field 

message: I have re-written and expanded the article to cover the notions of a purely inseparable extension, and that of the separable part of an algebraic extension, and to provide a more comprehensive treatment of separable extensions in their own right. The article also includes an "Informal discussion", which provides at least some basic background for the article, and a section solely on separable polynomials (which includes an example of an inseparable polynomial as requested in the section above). Any comments, suggestions, or further improvements would be very much welcome. PST 08:48, 9 April 2010 (UTC)
thread_title:  Major changes to article 

message: Why the repeated use of phrases like "non-zero prime" and "irreducible (non-zero) polynomial"? A prime element is by definition not zero. Similarly, a irreducible polynomial is by definition not constant, thus not zero. Not using the unnecessary "non-zero" phrase is exactly the "less is more" philosophy that is abstract algebra. Bender2k14 (talk) 00:54, 9 March 2011 (UTC)
replies: text: I think you'd have to ask the editor User:Point-set topologist why s/he thinks it's necessary to say non-zero all those times (this is the editor that wrote all of these, see the diff  and all the following ones). Perhaps s/he was confused with prime elements versus prime ideals (the non-zero ones of the latter correspond to the former in the case at hand). Also, I'm pretty sure not saying unnecessary things is an idea that pervades much of mathematics. RobHar (talk) 04:33, 9 March 2011 (UTC)
replies: text: You are absolutely right, RobHar. I will work to remove "non-zero" where unnecessary. Thank you for pointing this out! --PST 22:35, 29 September 2011 (UTC)
thread_title:  Use of phrase "non-zero" 

message: As discussed in https://en.wikipedia.org/wiki/Talk:Separable_polynomial there are two approaches to defining a separable polynomial, and the modern one is to require (deg f) distinct roots.
Currently the article claims equivalence of the following claims:
The constant 1 is a polynomial greatest common divisor of f and f'.[7]
The formal derivative f' of f is not the zero polynomial.[8]
Note that in the source itself these are never said to be equivalent, the first is said to be equivalent to the modern definition of separability (which has a different name in the source), the second to the old definition (which the source calls separable).
These two claims are obviously not equivalent, and their equivalence is not actually supported by the source. Could the edit https://en.wikipedia.org/w/index.php?title=Separable_extension&diff=853049965&oldid=853019569 be undone?  — Preceding unsigned comment added by 2A09:80C0:192:0:58C8:11AD:1DF:87ED (talk) 14:30, 24 October 2019 (UTC)
replies: text: The article does not claim the equivalence of these assertions for general polynomials. It claims only this equivalence for irreducible polynomials and minimal polynomials (which are necessarily irreductible). Indeed this equivalence is true for irreducible polynomials. So, there is nothing wrong in the article. However, I'll edit the article for emphasizing that the equivalence applies only to irreducible polynomials. D.Lazard (talk) 15:32, 24 October 2019 (UTC)
thread_title:  Old and new definition of separability