Question

How do the proper ideals of $\Bbb Q[x]/ \langle x^3 \rangle$ look like?

score 91 · Answer 1 · 2026-04-14 20:38:37

91

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How do the proper ideals of $\Bbb Q[x]/ \langle x^3 \rangle$ look like?

Published on 14 Apr 2026 - 20:38

score 314 · Answer 2 · 2026-04-15 03:54:17

314

Views

Show that every nonzero prime ideal in $\mathbb{C}[x, y]/(x^2 - y^2 - 1)$ is maximal

Published on 15 Apr 2026 - 3:54

score 1k · Answer 3 · 2026-04-15 13:20:49

1k

Views

Show that $\mathbb{Z}_3[i]$ is a field

Published on 15 Apr 2026 - 13:20

score 158 · Answer 4 · 2026-04-14 03:38:11

158

Views

Polynomial Evaluation. How to (formally) substitute X with a Matrix

Published on 14 Apr 2026 - 3:38

score 2.2k · Answer 5 · 2026-04-14 23:05:10

2.2k

Views

Factoring $x^n + 1$.

Published on 14 Apr 2026 - 23:05

score 979 · Answer 6 · 2026-04-15 22:33:08

979

Views

$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

Published on 15 Apr 2026 - 22:33

score 1.6k · Answer 7 · 2026-04-15 18:16:19

1.6k

Views

Given any commutative ring $R$ with unity, $R[X]$ has infinitely many maximal ideals.

Published on 15 Apr 2026 - 18:16

score 168 · Answer 8 · 2026-04-11 10:46:58

168

Views

Algorithm to find relations between polynomials

Published on 11 Apr 2026 - 10:46

score 109 · Answer 9 · 2026-04-16 15:04:18

109

Views

Show that $\mathbb{Z}_5[x]/(x^2+x+1)\cong\mathbb{Z}_5[x]/(x^2+x+2)$

Published on 16 Apr 2026 - 15:04

score 119 · Answer 10 · 2026-04-14 01:23:07

119

Views

Prove that any polynomial with integer coefficients must have a composite number in its image.

Published on 14 Apr 2026 - 1:23

score 670 · Answer 11 · 2026-04-10 19:39:45

670

Views

How many polynomials of degree $n$ in $\mathbb{Z}/3\mathbb{Z}$

Published on 10 Apr 2026 - 19:39

score 546 · Answer 12 · 2026-04-16 03:48:49

546

Views

For polynomials $f, g$ and $\gcd(f(X),g(X))=d(X)$ then $\gcd(f(X+a),g(X+a))=d(X+a)$

Published on 16 Apr 2026 - 3:48

score 46 · Answer 13 · 2026-04-16 01:36:07

46

Views

$\gcd(x,y)=1$ then $\gcd(c \cdot x, c \cdot y)=c$ for polynomials

Published on 16 Apr 2026 - 1:36

score 123 · Answer 14 · 2026-04-16 07:45:19

123

Views

What are the polynomial quotients $R/x$ and $R/(R/x)$ for $R = (\mathbb{R}[x]/x^n)$?

Published on 16 Apr 2026 - 7:45

score 109 · Answer 15 · 2026-04-14 20:34:51

109

Views

determining if quotient ring of polynomials over a finite field is a field or not

Published on 14 Apr 2026 - 20:34

List Question

How do the proper ideals of $\Bbb Q[x]/ \langle x^3 \rangle$ look like?

Show that every nonzero prime ideal in $\mathbb{C}[x, y]/(x^2 - y^2 - 1)$ is maximal

Show that $\mathbb{Z}_3[i]$ is a field

Polynomial Evaluation. How to (formally) substitute X with a Matrix

Factoring $x^n + 1$.

$\Bbb R[X,Y]/(F) \cong \Bbb R[Z]$ and $F_X G_Y - G_X F_Y \in \Bbb R^*$

Given any commutative ring $R$ with unity, $R[X]$ has infinitely many maximal ideals.

Algorithm to find relations between polynomials

Show that $\mathbb{Z}_5[x]/(x^2+x+1)\cong\mathbb{Z}_5[x]/(x^2+x+2)$

Prove that any polynomial with integer coefficients must have a composite number in its image.

How many polynomials of degree $n$ in $\mathbb{Z}/3\mathbb{Z}$

For polynomials $f, g$ and $\gcd(f(X),g(X))=d(X)$ then $\gcd(f(X+a),g(X+a))=d(X+a)$

$\gcd(x,y)=1$ then $\gcd(c \cdot x, c \cdot y)=c$ for polynomials

What are the polynomial quotients $R/x$ and $R/(R/x)$ for $R = (\mathbb{R}[x]/x^n)$?

determining if quotient ring of polynomials over a finite field is a field or not

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