List questions from maximal-and-prime-ideals

Published on 10 Apr 2015 - 18:06

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Prime Ideals and multiplicative sets

Published on 11 Apr 2015 - 12:02

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Element in no prime ideal $\iff$ it is a unit

Published on 12 Apr 2015 - 3:22

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True or false question about polynomial ring

Published on 13 Apr 2015 - 16:14

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How can I verify that the ideal $(x^2-zw, z^2-yw, y^3-xw, w^3-xy^2z)$ is prime in $\mathbb Q[x,y,z,w]$?

Published on 14 Apr 2015 - 8:47

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What does it mean for a prime ideal to divide a natural number m?

Published on 27 Mar 2026 - 16:47

316

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Diophantine equation $x^2 + 6(y+1)^2 = (y+2)^3$

Published on 16 Apr 2015 - 22:01

702

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Prove that $I[x]$ is not maximal in $R[x]$.

Published on 17 Apr 2015 - 1:25

270

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Show that $I = \{a +\sqrt2b \in \Bbb Z[\sqrt2] : a$ and $b$ are both multiple of $5\}$ is a maximal ideal.

Published on 17 Apr 2015 - 16:17

165

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Is $ \langle x,5 \rangle $ a maximal ideal of $ \mathbb{Z}[x] $?

Published on 18 Apr 2015 - 6:43

689

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Maximal ideals of the ring of matrices

Published on 18 Apr 2015 - 18:13

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$A$ prime in $S$ implies that $\phi^{-1}(A)$ prime in $R$ ; $A$ maximal in $S$ implies that $\phi^{-1}(A)$ maximal in $R$

Published on 19 Apr 2015 - 3:51

133

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Let $R$ be a PID and $I$ a prime ideal of $R$ s.t. $0 \subset I \subset 1_R$

Published on 29 Mar 2026 - 22:42

186

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Relation between reduced finite algebra, prime ideal and field extension

Published on 20 Apr 2015 - 6:16

98

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Show that $\bar{a}_{n}(\bar{x})^n+···+\bar{a}_{1}\bar{x}+\bar{a}_{0}=0_{F[x]/I}$

Published on 20 Apr 2015 - 19:49

List Question

All prime ideals are maximal - Counterexample

Prime Ideals and multiplicative sets

Element in no prime ideal $\iff$ it is a unit

True or false question about polynomial ring

How can I verify that the ideal $(x^2-zw, z^2-yw, y^3-xw, w^3-xy^2z)$ is prime in $\mathbb Q[x,y,z,w]$?

What does it mean for a prime ideal to divide a natural number m?

Diophantine equation $x^2 + 6(y+1)^2 = (y+2)^3$

Prove that $I[x]$ is not maximal in $R[x]$.

Show that $I = \{a +\sqrt2b \in \Bbb Z[\sqrt2] : a$ and $b$ are both multiple of $5\}$ is a maximal ideal.

Is $ \langle x,5 \rangle $ a maximal ideal of $ \mathbb{Z}[x] $?

Maximal ideals of the ring of matrices

$A$ prime in $S$ implies that $\phi^{-1}(A)$ prime in $R$ ; $A$ maximal in $S$ implies that $\phi^{-1}(A)$ maximal in $R$

Let $R$ be a PID and $I$ a prime ideal of $R$ s.t. $0 \subset I \subset 1_R$

Relation between reduced finite algebra, prime ideal and field extension

Show that $\bar{a}_{n}(\bar{x})^n+···+\bar{a}_{1}\bar{x}+\bar{a}_{0}=0_{F[x]/I}$

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