List questions from field-theory

Published on 11 Apr 2026 - 21:38

30

Views

Regarding nomenclature of a vector related to field automorphisms

Published on 13 Apr 2026 - 0:46

875

Views

Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

Published on 13 Apr 2026 - 4:39

37

Views

Separable polynomial and algebraic extension

Published on 12 Apr 2026 - 10:52

1.9k

Views

Finding the order of elements in a Galois Field

Published on 12 Apr 2026 - 9:14

272

Views

Proper Field extensions

Published on 12 Apr 2026 - 4:35

129

Views

There are no field structures on $\mathbb{R}^3$, but what of $\mathbb{R}^n$ for $n\geq 4$?

Published on 11 Apr 2026 - 21:12

176

Views

Can the natural embedding $K\to K[X]/(f)$ be extended to form an isomorphism $L/K\to K[X]/(f)$?

Published on 30 Aug 2014 - 11:20

568

Views

Galois group of $X^{5}-2X+7$ over $\mathbb{Q}$

Published on 04 Apr 2026 - 5:41

114

Views

Separable extension

Published on 13 Apr 2026 - 0:52

306

Views

Is there a short proof of the formula for Legendre symbol $(\frac{2}{p})=(-1)^{(p^2-1)/8}$?

Published on 26 Mar 2026 - 23:10

63

Views

If $Q$ is a prime ideal of $R[x]$ then $QF[x]\cap R[x]=Q$

Published on 25 Mar 2026 - 17:21

270

Views

Finite dimensional field extension, finitely many intermediate fields

Published on 01 Sep 2014 - 8:18

77

Views

Galois group of order 2^4

Published on 04 Apr 2026 - 5:40

57

Views

Minimal polynomial (Field theory)

Published on 12 Apr 2026 - 4:09

List Question

Fields - Proof that every multiple of zero equals zero

Regarding nomenclature of a vector related to field automorphisms

Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

Separable polynomial and algebraic extension

Finding the order of elements in a Galois Field

Proper Field extensions

There are no field structures on $\mathbb{R}^3$, but what of $\mathbb{R}^n$ for $n\geq 4$?

Can the natural embedding $K\to K[X]/(f)$ be extended to form an isomorphism $L/K\to K[X]/(f)$?

Galois group of $X^{5}-2X+7$ over $\mathbb{Q}$

Separable extension

Is there a short proof of the formula for Legendre symbol $(\frac{2}{p})=(-1)^{(p^2-1)/8}$?

If $Q$ is a prime ideal of $R[x]$ then $QF[x]\cap R[x]=Q$

Finite dimensional field extension, finitely many intermediate fields

Galois group of order 2^4

Minimal polynomial (Field theory)

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