Question

A polynomial over $A[z]/(z^2-a)$ can be "completed" to a polynomial over $A$

score 37 · Answer 1 · 2026-04-12 17:28:15

37

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A polynomial over $A[z]/(z^2-a)$ can be "completed" to a polynomial over $A$

Published on 12 Apr 2026 - 17:28

score 604 · Answer 2 · 2026-04-13 16:05:18

604

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Finding the multiplicative inverse of a field extension

Published on 13 Apr 2026 - 16:05

score 79 · Answer 3 · 2026-04-17 03:38:39

79

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Consider $p(x)=x^4 -2x^2 -2 \in \mathbb{Q}[x]$.

Published on 17 Apr 2026 - 3:38

score 596 · Answer 4 · 2026-04-23 17:31:53

596

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Let $p$ be a prime and $k$a positive ingeger such that $a^k=a (mod p)$ for all integers a. prove that $p-1$divides $k-1$

Published on 23 Apr 2026 - 17:31

score 140 · Answer 5 · 2026-04-09 20:37:15

140

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Let $H$ be a group, $H_{ab}$ its abelianization. Is $Hom(H, \Bbb Z) \cong Hom(H_{ab}, \Bbb Z)$?

Published on 09 Apr 2026 - 20:37

score 104 · Answer 6 · 2026-05-10 12:32:48

104

Views

Is this ring an integral domain? Prove or give a counterexample

Published on 10 May 2026 - 12:32

score 958 · Answer 7 · 2026-05-10 14:06:21

958

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Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

Published on 10 May 2026 - 14:06

score 50 · Answer 8 · 2026-05-10 16:13:41

50

Views

Prove that if $x^2 +\bar ax +\bar 1$ has a double root, then $(\mathbb Z/5)[x]/I$ $\cong$ $(\mathbb Z/5)[x]/(x^2)$ where I = $x^2 +\bar ax +\bar 1$

Published on 10 May 2026 - 16:13

score 823 · Answer 9 · 2026-04-11 13:13:25

823

Views

Will $Z[X] / (x^2 +1)$ be a PID?

Published on 11 Apr 2026 - 13:13

score 249 · Answer 10 · 2026-04-16 10:45:03

249

Views

Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

Published on 16 Apr 2026 - 10:45

score 329 · Answer 11 · 2026-04-12 12:02:56

329

Views

Can the skew field of quaternions be seen as an extension over $\Bbb C$

Published on 12 Apr 2026 - 12:02

score 141 · Answer 12 · 2026-04-15 18:13:51

Construct a faithful injective module over the group algebra $KG$ where $K$ is a field and $G$ is arbitrary group.

score 150 · Answer 13 · 2026-05-13 14:37:06

150

Views

Properties of Groebner bases

Published on 13 May 2026 - 14:37

score 110 · Answer 14 · 2026-05-10 12:34:08

110

Views

If every proper overring of $R$ is a valuation domain, then $R$ is a valuation domain?

Published on 10 May 2026 - 12:34

score 197 · Answer 15 · 2026-04-14 06:19:12

197

Views

Ideal generated by $1+2i$ is the same as $(a+bi|a, b \in \mathbb{Z}, 2a=b mod 5)$ in the ring $\mathbb{Z}[i]$ = ($a+bi|a, b \in \mathbb{Z}$

Published on 14 Apr 2026 - 6:19

List Question

A polynomial over $A[z]/(z^2-a)$ can be "completed" to a polynomial over $A$

Finding the multiplicative inverse of a field extension

Consider $p(x)=x^4 -2x^2 -2 \in \mathbb{Q}[x]$.

Let $p$ be a prime and $k$a positive ingeger such that $a^k=a (mod p)$ for all integers a. prove that $p-1$divides $k-1$

Let $H$ be a group, $H_{ab}$ its abelianization. Is $Hom(H, \Bbb Z) \cong Hom(H_{ab}, \Bbb Z)$?

Is this ring an integral domain? Prove or give a counterexample

Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

Prove that if $x^2 +\bar ax +\bar 1$ has a double root, then $(\mathbb Z/5)[x]/I$ $\cong$ $(\mathbb Z/5)[x]/(x^2)$ where I = $x^2 +\bar ax +\bar 1$

Will $Z[X] / (x^2 +1)$ be a PID?

Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

Can the skew field of quaternions be seen as an extension over $\Bbb C$

Construct a faithful injective module over the group algebra $KG$ where $K$ is a field and $G$ is arbitrary group.

Properties of Groebner bases

If every proper overring of $R$ is a valuation domain, then $R$ is a valuation domain?

Ideal generated by $1+2i$ is the same as $(a+bi|a, b \in \mathbb{Z}, 2a=b mod 5)$ in the ring $\mathbb{Z}[i]$ = ($a+bi|a, b \in \mathbb{Z}$

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