Question

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

score 88 · Answer 1 · 2018-08-03 05:17:21

88

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

Published on 03 Aug 2018 - 5:17

score 311 · Answer 2 · 2018-08-10 01:49:14

311

Views

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

Published on 10 Aug 2018 - 1:49

score 1k · Answer 3 · 2018-08-10 03:32:27

1k

Views

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

Published on 10 Aug 2018 - 3:32

score 155 · Answer 4 · 2018-08-19 10:47:15

155

Views

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

Published on 19 Aug 2018 - 10:47

score 2.2k · Answer 5 · 2018-08-24 03:53:31

2.2k

Views

Factoring $x^n + 1$.

Published on 24 Aug 2018 - 3:53

score 976 · Answer 6 · 2018-08-26 05:52:16

976

Views

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

Published on 26 Aug 2018 - 5:52

score 1.6k · Answer 7 · 2018-08-26 07:09:17

1.6k

Views

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

Published on 26 Aug 2018 - 7:09

score 165 · Answer 8 · 2018-09-02 11:12:59

165

Views

Algorithm to find relations between polynomials

Published on 02 Sep 2018 - 11:12

score 106 · Answer 9 · 2018-09-18 22:18:57

106

Views

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

Published on 18 Sep 2018 - 22:18

score 116 · Answer 10 · 2018-10-10 11:41:35

116

Views

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

Published on 10 Oct 2018 - 11:41

score 667 · Answer 11 · 2018-10-10 22:52:11

667

Views

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

Published on 10 Oct 2018 - 22:52

score 543 · Answer 12 · 2018-10-11 11:03:02

543

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 11 Oct 2018 - 11:03

score 43 · Answer 13 · 2018-10-11 13:49:34

43

Views

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

Published on 11 Oct 2018 - 13:49

score 120 · Answer 14 · 2018-10-13 20:26:57

120

Views

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

Published on 13 Oct 2018 - 20:26

score 106 · Answer 15 · 2018-10-16 12:57:13

106

Views

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

Published on 16 Oct 2018 - 12:57

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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