Question

Are there any non-trivial nilpotent and idempotent in the ring $F[X,Y]/(X^2-Y^2)$, where $F$ is a field?

score 85 · Answer 1 · 2026-04-16 02:34:33

Are there any non-trivial nilpotent and idempotent in the ring $F[X,Y]/(X^2-Y^2)$, where $F$ is a field?

Published on 16 Apr 2026 - 2:34

score 137 · Answer 2 · 2026-04-15 22:22:16

Splitting field of $ f(x) = x^4 - 2 $ over $ \Bbb{Q} $ with minimal Galois theory and avoiding the use of embedding in $ \Bbb{C} $.

score 43 · Answer 3 · 2026-05-16 11:49:15

43

Views

If $L/K$ is abelian with exponent $n$, then $L=K(\sqrt[n]{\Delta})$ with $\Delta=K^\cap L^{n}$

Published on 16 May 2026 - 11:49

score 52 · Answer 4 · 2026-04-16 20:58:27

52

Views

Roots of irreducible polynomial $f(x)=x^4+x^3+x^2+x+1$ in $GF(2^4)$ having defining polynomial $x^4+x+1$

Published on 16 Apr 2026 - 20:58

score 34 · Answer 5 · 2026-04-16 04:47:03

34

Views

Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

Published on 16 Apr 2026 - 4:47

score 57 · Answer 6 · 2026-04-17 10:35:07

57

Views

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Published on 17 Apr 2026 - 10:35

score 92 · Answer 7 · 2026-04-24 11:23:53

92

Views

Is there a field $k$ in which $x^3+3$ has double roots?

Published on 24 Apr 2026 - 11:23

score 70 · Answer 8 · 2026-04-18 13:00:57

70

Views

Show if $a^{12} = e$ so $(a+a^{-1})^2 = 3$

Published on 18 Apr 2026 - 13:00

score 174 · Answer 9 · 2026-04-16 06:32:39

174

Views

Determine the Galois group of $x^4 -4x^2+2$

Published on 16 Apr 2026 - 6:32

score 98 · Answer 10 · 2026-04-15 03:15:12

98

Views

Interpreting Galois theory: symmetry of i and -i, symmetry of $\sqrt{2}$ and $-\sqrt{2}$

Published on 15 Apr 2026 - 3:15

score 67 · Answer 11 · 2026-04-13 09:48:00

67

Views

is my proof regarding the Zeros of polynomial over an infinite field correct?

Published on 13 Apr 2026 - 9:48

score 110 · Answer 12 · 2026-04-14 20:32:48

110

Views

Let $K$ be a field of characteristic $p$. Show $\mathbb{F}_p[a] \cong \mathbb{F}_p[b]$ for elements $a,b\in K^\times$ of the same order.

Published on 14 Apr 2026 - 20:32

score 153 · Answer 13 · 2026-05-15 13:15:02

153

Views

$b$ not a square, $a^2 − b$ a square Why is $\Bbb Q(\sqrt {a + \sqrt b})$ the splitting field of $f(x)=(t^2-a)^2-b$ and a normal extension?

Published on 15 May 2026 - 13:15

score 66 · Answer 14 · 2026-04-16 06:18:13

66

Views

Is $\mathbb{C}/\mathbb{Q}$ a simple field extension?

Published on 16 Apr 2026 - 6:18

score 72 · Answer 15 · 2026-04-15 04:08:26

72

Views

What's the 2-adic analogue of $SL_2(\Bbb R)$ factoring through the quotient $PSL(2,\Bbb R)$?

Published on 15 Apr 2026 - 4:08

List Question

Are there any non-trivial nilpotent and idempotent in the ring $F[X,Y]/(X^2-Y^2)$, where $F$ is a field?

Splitting field of $ f(x) = x^4 - 2 $ over $ \Bbb{Q} $ with minimal Galois theory and avoiding the use of embedding in $ \Bbb{C} $.

If $L/K$ is abelian with exponent $n$, then $L=K(\sqrt[n]{\Delta})$ with $\Delta=K^\cap L^{n}$

Roots of irreducible polynomial $f(x)=x^4+x^3+x^2+x+1$ in $GF(2^4)$ having defining polynomial $x^4+x+1$

Is the field $L = \mathbb{Q}( \sqrt{2 + \sqrt{2}})$ normal over $K=\mathbb{Q}$?

Splitting field of $f(x) = x^6 +x^4 +x^2 + 1 ∈ K[x]$ over (a) $K = \mathbb{Q}$, (b) $K = \mathbb{F}_5$

Is there a field $k$ in which $x^3+3$ has double roots?

Show if $a^{12} = e$ so $(a+a^{-1})^2 = 3$

Determine the Galois group of $x^4 -4x^2+2$

Interpreting Galois theory: symmetry of i and -i, symmetry of $\sqrt{2}$ and $-\sqrt{2}$

is my proof regarding the Zeros of polynomial over an infinite field correct?

Let $K$ be a field of characteristic $p$. Show $\mathbb{F}_p[a] \cong \mathbb{F}_p[b]$ for elements $a,b\in K^\times$ of the same order.

$b$ not a square, $a^2 − b$ a square Why is $\Bbb Q(\sqrt {a + \sqrt b})$ the splitting field of $f(x)=(t^2-a)^2-b$ and a normal extension?

Is $\mathbb{C}/\mathbb{Q}$ a simple field extension?

What's the 2-adic analogue of $SL_2(\Bbb R)$ factoring through the quotient $PSL(2,\Bbb R)$?

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