List questions from field-theory | MathQA

Matrix $A$ of multiplication with some $a$ in a field extension $K/F$ for some basis of $K$. Show that $a$ is a root of the characteristic polynomial.

Published on 15 Apr 2026 - 6:57

Set of all algebraic numbers A(C;Q) has no finite extension

Published on 15 Apr 2026 - 18:27

Adjoining Root over Z/2

Published on 13 Apr 2026 - 10:19

Roots of cubic equations in field of characteristic $3$

Published on 16 Apr 2026 - 1:43

Fixed field of the linear fractional maps ($X \to \frac{aX+b}{cX+d}$) of $k(X)$ where $k$ is finite.

Published on 11 May 2026 - 8:42

How is this proof correct (takes $a$ to be a specific number)?

Published on 14 Apr 2026 - 8:27

Deducing that $\mathbb Z[2 \sqrt{2}]$ is not a $UFD.$

Published on 15 May 2026 - 21:04

How to identify transcendental numbers?

Published on 10 Apr 2026 - 14:49

why if I proved it for $\mathbb Q[\sqrt{-2}],$ it will be correct for $\mathbb Q(\sqrt{-2}),$?

Published on 16 Apr 2026 - 4:00

How to prove the additive inverse of 0 is 0?

Published on 11 Apr 2026 - 17:26

Find the set $\{a^n\,|\,n\geq1\}$ which $F$ is a field of order 32 and $a\in F$ that is not zero and one of the field

Published on 17 Apr 2026 - 11:08

Why $(\mathbb F_2 [x] / (x^3 + x +1))^×$ has order 7?

Published on 17 Apr 2026 - 5:00

When does a polynomial with coefficients in $\mathbb{Z}[x_1,x_2,\dots, x_d]$ have factors with integer coefficients?

Published on 15 Apr 2026 - 22:51

union of fix points of $f\in\operatorname{Gal}(K/F)\setminus\{1\}$ is a proper subset of $K$

Published on 13 Apr 2026 - 19:13

Why the number of elements of $ Z$ of order $d$ is $\varphi (d)$?

Published on 15 Apr 2026 - 18:27