Question

Adding a prime number to a special homogeneous prime ideal preserves primeness

score 55 · Answer 1 · 2026-04-14 08:44:49

55

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Adding a prime number to a special homogeneous prime ideal preserves primeness

Published on 14 Apr 2026 - 8:44

score 554 · Answer 2 · 2026-04-11 23:33:19

554

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$\mathbb Z[x]/(9x^2+1)$ has a prime ideal which is not maximal

Published on 11 Apr 2026 - 23:33

score 2.7k · Answer 3 · 2026-04-29 12:23:53

2.7k

Views

Proving a prime ideal is maximal in a PID

Published on 29 Apr 2026 - 12:23

score 1.5k · Answer 4 · 2026-04-15 23:22:08

1.5k

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All prime ideals of $\mathbf{R}[x,y]$ and $\mathbf{C}[x, y]$.

Published on 15 Apr 2026 - 23:22

score 23 · Answer 5 · 2026-04-14 09:56:56

23

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Working out prime ideals in $\mathbb{Z}_{30}$

Published on 14 Apr 2026 - 9:56

score 1.2k · Answer 6 · 2026-05-02 20:18:13

1.2k

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Let $F[[X]]$ be the ring of formal power series over the field $F$. Show that $(X)$ is a maximal ideal.

Published on 02 May 2026 - 20:18

score 61 · Answer 7 · 2026-04-16 04:24:12

61

Views

A property similar to compactly packed

Published on 16 Apr 2026 - 4:24

score 210 · Answer 8 · 2026-04-30 13:45:09

210

Views

Given a prime ideal $P$ in a valuation ring $A$, there is a valuation ring $B$ containing $A$ such that $B/PB$ is the fraction field of $A/P$ ?

Published on 30 Apr 2026 - 13:45

score 804 · Answer 9 · 2026-04-29 12:42:22

804

Views

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Published on 29 Apr 2026 - 12:42

score 942 · Answer 10 · 2026-04-14 11:07:46

942

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Valuation ring lying between a valuation ring and its fraction field

Published on 14 Apr 2026 - 11:07

score 196 · Answer 11 · 2026-04-18 08:53:03

196

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Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Published on 18 Apr 2026 - 8:53

score 177 · Answer 12 · 2026-04-29 12:24:22

177

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Corollary of Proposition 11 in Lang's Algebraic Number Theory

Published on 29 Apr 2026 - 12:24

score 835 · Answer 13 · 2026-04-14 18:45:33

835

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Show that $(n,x)$ is a prime ideal if and only if $n$ is a prime number $(R = \mathbb{Z}[x],n\geq 1$)

Published on 14 Apr 2026 - 18:45

score 1.9k · Answer 14 · 2026-04-13 15:43:54

1.9k

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Ideals of the ring of rational numbers with odd denominators

Published on 13 Apr 2026 - 15:43

score 1k · Answer 15 · 2026-04-13 02:01:42

1k

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If $ U$ is maximal among non-principal ideals show that $U$ is prime. (Hints?)

Published on 13 Apr 2026 - 2:01

List Question

Adding a prime number to a special homogeneous prime ideal preserves primeness

$\mathbb Z[x]/(9x^2+1)$ has a prime ideal which is not maximal

Proving a prime ideal is maximal in a PID

All prime ideals of $\mathbf{R}[x,y]$ and $\mathbf{C}[x, y]$.

Working out prime ideals in $\mathbb{Z}_{30}$

Let $F[[X]]$ be the ring of formal power series over the field $F$. Show that $(X)$ is a maximal ideal.

A property similar to compactly packed

Given a prime ideal $P$ in a valuation ring $A$, there is a valuation ring $B$ containing $A$ such that $B/PB$ is the fraction field of $A/P$ ?

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Valuation ring lying between a valuation ring and its fraction field

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Corollary of Proposition 11 in Lang's Algebraic Number Theory

Show that $(n,x)$ is a prime ideal if and only if $n$ is a prime number $(R = \mathbb{Z}[x],n\geq 1$)

Ideals of the ring of rational numbers with odd denominators

If $ U$ is maximal among non-principal ideals show that $U$ is prime. (Hints?)

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