Talk:root field

Definition
@AugPi Where did you get this definition from? I know the root field as the smallest extension where the polynomial has one root (i.e., is reducible), not where it decomposes into linear factors. 𝟙𝟤𝟯𝟺𝐪𝑤𝒆𝓇𝟷𝟮𝟥𝟜𝓺𝔴𝕖𝖗𝟰 (𝗍𝗮𝘭𝙠) 16:07, 30 April 2022 (UTC)
 * According to (i), the extension N splits the polynomial f(x) (or “f(x) splits over N”), and according to (ii), N is the smallest extension of F which splits f(x), &there4; the “root field” N qualifies as a splitting field.  AugPi 16:16, 6 May 2022 (UTC)
 * According to (i), the extension N splits the polynomial f(x) (or “f(x) splits over N”), and according to (ii), N is the smallest extension of F which splits f(x), &there4; the “root field” N qualifies as a splitting field.  AugPi 16:16, 6 May 2022 (UTC)