Question

For which $p$ and $q$ polynomials $x^q-1$ and $(x+1)^q-1$ are coprime in $F_p[x]$?

score 247 · Answer 1 · 2026-04-17 06:32:54

247

Views

For which $p$ and $q$ polynomials $x^q-1$ and $(x+1)^q-1$ are coprime in $F_p[x]$?

Published on 17 Apr 2026 - 6:32

score 780 · Answer 2 · 2026-04-13 04:16:19

780

Views

Is $S = \{(a,b) \mid a + b = 0\}$ a subring of $\mathbb Z \times \mathbb Z$?

Published on 13 Apr 2026 - 4:16

score 111 · Answer 3 · 2026-04-14 16:59:53

111

Views

Find all ideals of $K \times K$ where K is a field

Published on 14 Apr 2026 - 16:59

score 842 · Answer 4 · 2026-04-12 10:28:51

842

Views

Product of two non-principal ideals

Published on 12 Apr 2026 - 10:28

score 35 · Answer 5 · 2026-04-15 18:51:33

35

Views

If $k$ is a field then $\text{End}_k(k^2)$ is simple

Published on 15 Apr 2026 - 18:51

score 7.8k · Answer 6 · 2026-04-14 16:05:00

7.8k

Views

A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal

Published on 14 Apr 2026 - 16:05

score 1.9k · Answer 7 · 2026-04-14 05:31:42

1.9k

Views

Proving that the forgetful functor $U:\mathbf{Ring}\to\mathbf{Set}$ is representable.

Published on 14 Apr 2026 - 5:31

score 234 · Answer 8 · 2026-04-11 20:40:09

234

Views

Will $\mathbb Z/{mn}\simeq \mathbb Z/m\times\mathbb Z/n$ as rings if $(m, n)=1$

Published on 11 Apr 2026 - 20:40

score 45 · Answer 9 · 2026-04-13 08:23:08

45

Views

Question concerning the dedekind factoring of a principal ideal

Published on 13 Apr 2026 - 8:23

score 110 · Answer 10 · 2026-04-15 00:24:52

110

Views

Show that a simple ring is always an algebra over some field

Published on 15 Apr 2026 - 0:24

score 108 · Answer 11 · 2026-04-12 15:54:18

108

Views

A question about a quotient ring.

Published on 12 Apr 2026 - 15:54

score 566 · Answer 12 · 2026-04-13 04:37:10

566

Views

Why is ring of integers $\mathcal O_K$ called ring of integers - what properties of $\mathbb{Z}$ does it inherit?

Published on 13 Apr 2026 - 4:37

score 131 · Answer 13 · 2026-04-13 01:11:35

131

Views

uniqueness Euclidean Norm in Euclidean domain

Published on 13 Apr 2026 - 1:11

score 56 · Answer 14 · 2026-04-16 01:53:07

56

Views

Show that $\overline{x}\in\Bbb Z/(n\Bbb Z)$ is invertible iff $\gcd(x,n)=1$

Published on 16 Apr 2026 - 1:53

score 77 · Answer 15 · 2026-04-10 20:49:35

77

Views

How do you calculate this product $\mathbb{Z}_6\times\mathbb{Z}_6$

Published on 10 Apr 2026 - 20:49

List Question

For which $p$ and $q$ polynomials $x^q-1$ and $(x+1)^q-1$ are coprime in $F_p[x]$?

Is $S = \{(a,b) \mid a + b = 0\}$ a subring of $\mathbb Z \times \mathbb Z$?

Find all ideals of $K \times K$ where K is a field

Product of two non-principal ideals

If $k$ is a field then $\text{End}_k(k^2)$ is simple

A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal

Proving that the forgetful functor $U:\mathbf{Ring}\to\mathbf{Set}$ is representable.

Will $\mathbb Z/{mn}\simeq \mathbb Z/m\times\mathbb Z/n$ as rings if $(m, n)=1$

Question concerning the dedekind factoring of a principal ideal

Show that a simple ring is always an algebra over some field

A question about a quotient ring.

Why is ring of integers $\mathcal O_K$ called ring of integers - what properties of $\mathbb{Z}$ does it inherit?

uniqueness Euclidean Norm in Euclidean domain

Show that $\overline{x}\in\Bbb Z/(n\Bbb Z)$ is invertible iff $\gcd(x,n)=1$

How do you calculate this product $\mathbb{Z}_6\times\mathbb{Z}_6$

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