List questions from maximal-and-prime-ideals

Published on 25 Mar 2026 - 17:38

237

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The ideal $\langle x^2+1, y-1 \rangle$ in $\mathbb{Q}[x,y]$

Published on 18 May 2020 - 14:33

281

Views

Primes which can be Norms vs Primes which Split Completely in Galois Extensions

Published on 29 Mar 2026 - 12:05

1.2k

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Finding class number of quadratic number field using Minkowski bound

Published on 25 Mar 2026 - 3:01

67

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Descending chaincondition for cyclic ideals

Published on 19 May 2020 - 16:28

119

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Factorization into prime ideals in dedekind domain $\mathbb{C}[t]_{(t)}[x]/(x^3+x^2+t)$

Published on 25 Mar 2026 - 20:41

349

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Number of maximal ideals in the ring $\mathbb{Z}_5[x]/\langle (x+1)^2(x+2)^3 \rangle$

Published on 20 May 2020 - 12:04

206

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If $I$ is a proper ideal not prime, there exists $J,K$ such that $J\subsetneq I$, $K\subsetneq I$ and $JK\subseteq I$

Published on 26 Mar 2026 - 11:01

29

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well-definedness of closed set in Zariski topology

Published on 25 Mar 2026 - 17:19

137

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How to finish this argument showing preimage of maximal ideal is maximal under surjective map.

Published on 23 May 2020 - 17:42

197

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surjectivity condition for induced map of prime ideals

Published on 26 Mar 2026 - 2:46

124

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Why isn't $\{0\}$ being prime ideal is not maximal in $\mathbb{Z}$?

Published on 24 May 2020 - 20:47

125

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A problem regarding a maximal ideal in a polynomial ring in several variables

Published on 30 Mar 2026 - 8:27

929

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Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

Published on 25 Mar 2026 - 10:55

61

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Showing an ideal is prime in polynomial ring: over $\Bbb Q$ and $\Bbb C$.

Published on 30 Mar 2026 - 8:30

List Question

Show that $R[X]/(f)$ is Dedekind domain

The ideal $\langle x^2+1, y-1 \rangle$ in $\mathbb{Q}[x,y]$

Primes which can be Norms vs Primes which Split Completely in Galois Extensions

Finding class number of quadratic number field using Minkowski bound

Descending chaincondition for cyclic ideals

Factorization into prime ideals in dedekind domain $\mathbb{C}[t]_{(t)}[x]/(x^3+x^2+t)$

Number of maximal ideals in the ring $\mathbb{Z}_5[x]/\langle (x+1)^2(x+2)^3 \rangle$

If $I$ is a proper ideal not prime, there exists $J,K$ such that $J\subsetneq I$, $K\subsetneq I$ and $JK\subseteq I$

well-definedness of closed set in Zariski topology

How to finish this argument showing preimage of maximal ideal is maximal under surjective map.

surjectivity condition for induced map of prime ideals

Why isn't $\{0\}$ being prime ideal is not maximal in $\mathbb{Z}$?

A problem regarding a maximal ideal in a polynomial ring in several variables

Prove: $R$ is local $\iff$ $R$ has exactly one maximal ideal.

Showing an ideal is prime in polynomial ring: over $\Bbb Q$ and $\Bbb C$.

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