Show that the zeros of some polynomial in $\mathbb{Q}\left[T_1, \ldots T_r\right]$ has at point whose coordinates are in finite extension field of $Q$

score 45 · Answer 12 · 2026-04-14 00:01:39

45

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Elements in the field extension by adjoining a countable set of indeterminates to base field

Published on 14 Apr 2026 - 0:01

score 89 · Answer 13 · 2026-05-15 12:00:19

89

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Compute degree of $\mathbb Q(\zeta_8)$ over $\mathbb Q(\sqrt 2)$ and find a basis.

Published on 15 May 2026 - 12:00

score 62 · Answer 14 · 2026-05-15 02:43:18

62

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Compute $[ \mathbb Q(\zeta_8) : \mathbb Q(i)]$ and find a basis for the extension.

Published on 15 May 2026 - 2:43

score 59 · Answer 15 · 2026-04-12 12:40:33

59

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Assumption of commutativity in proof that a polynomial of degree $n$ can have at most $n$ roots in any extension field

Published on 12 Apr 2026 - 12:40

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Show that the zeros of some polynomial in $\mathbb{Q}\left[T_1, \ldots T_r\right]$ has at point whose coordinates are in finite extension field of $Q$

Elements in the field extension by adjoining a countable set of indeterminates to base field

Compute degree of $\mathbb Q(\zeta_8)$ over $\mathbb Q(\sqrt 2)$ and find a basis.

Compute $[ \mathbb Q(\zeta_8) : \mathbb Q(i)]$ and find a basis for the extension.

Assumption of commutativity in proof that a polynomial of degree $n$ can have at most $n$ roots in any extension field

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