Question

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

score 53 · Answer 1 · 2026-03-24 22:17:33

53

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

Published on 24 Mar 2026 - 22:17

score 552 · Answer 2 · 2026-03-25 13:55:13

552

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

Published on 25 Mar 2026 - 13:55

score 2.7k · Answer 3 · 2026-03-20 02:47:44

2.7k

Views

Proving a prime ideal is maximal in a PID

Published on 20 Mar 2026 - 2:47

score 1.5k · Answer 4 · 2026-03-25 06:05:56

1.5k

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

Published on 25 Mar 2026 - 6:05

score 20 · Answer 5 · 2026-03-17 09:17:03

20

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

Published on 17 Mar 2026 - 9:17

score 1.2k · Answer 6 · 2026-03-20 00:51:50

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 20 Mar 2026 - 0:51

score 59 · Answer 7 · 2026-03-25 11:53:19

59

Views

A property similar to compactly packed

Published on 25 Mar 2026 - 11:53

score 202 · Answer 8 · 2026-03-23 04:04:54

202

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 23 Mar 2026 - 4:04

score 793 · Answer 9 · 2026-03-22 17:31:00

793

Views

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

Published on 22 Mar 2026 - 17:31

score 941 · Answer 10 · 2026-03-25 11:53:20

941

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Valuation ring lying between a valuation ring and its fraction field

Published on 25 Mar 2026 - 11:53

score 194 · Answer 11 · 2026-03-24 22:07:43

194

Views

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

Published on 24 Mar 2026 - 22:07

score 171 · Answer 12 · 2026-03-20 04:19:03

171

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Corollary of Proposition 11 in Lang's Algebraic Number Theory

Published on 20 Mar 2026 - 4:19

score 833 · Answer 13 · 2026-03-25 13:34:19

833

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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 25 Mar 2026 - 13:34

score 1.9k · Answer 14 · 2026-03-17 14:23:33

1.9k

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Ideals of the ring of rational numbers with odd denominators

Published on 17 Mar 2026 - 14:23

score 1k · Answer 15 · 2018-03-03 04:03:14

1k

Views

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

Published on 03 Mar 2018 - 4:03

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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