Talk:Minimal polynomial (field theory)

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The very first sentence is nonsense

Latest comment: 1 year ago2 comments2 people in discussion

While one wants to avoid formalism in the first sentence, its current wording

"the minimal polynomial of an element α of a field is, roughly speaking, the polynomial of lowest degree having coefficients in the field, such that α is a root of the polynomial"

is nonsense as it speaks only of one single field. This way, the minimal polynomial is always just ${\displaystyle X-\alpha }$ . Should one mention the topics of extension field / subfield so early or simply write "in a smaller field"? Hagman (talk) 09:20, 13 October 2022 (UTC)Reply

Seems this was fixed on 11 January 2023 by User:128.131.42.63 -- 67.198.37.16 (talk) 22:07, 20 February 2024 (UTC)Reply

The Galois Extension example

Latest comment: 6 days ago1 comment1 person in discussion

In the first example giving a formula for the min poly in the context of a Galois extension, it is stated that one could replace ${\displaystyle G}$  with ${\displaystyle G/N}$ , where ${\displaystyle N}$  is the stabiliser of ${\displaystyle \alpha }$ . But, unless mistaken, ${\displaystyle N}$  isn't necessarily a normal subgroup, so what's written may be wrong? 82.69.22.30 (talk) 23:25, 22 August 2025 (UTC)Reply