Question

Prime ideals of the ring of integers of an algebraic number field

score 5.5k · Answer 1 · 2026-03-25 14:35:53

5.5k

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Prime ideals of the ring of integers of an algebraic number field

Published on 25 Mar 2026 - 14:35

score 9.3k · Answer 2 · 2014-11-22 22:39:15

9.3k

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Prove every prime ideal of a ring is a radical ideal.

Published on 22 Nov 2014 - 22:39

score 92 · Answer 3 · 2014-11-23 04:48:35

92

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Prove $\text{rad}(I)/I$ is isomorphic to $\mathfrak{N}(R/I)$

Published on 23 Nov 2014 - 4:48

score 36 · Answer 4 · 2014-11-23 16:41:03

36

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How to show that if $\gamma \alpha=0$ (mod $A$) then $\alpha = 0$ (mod $A$)

Published on 23 Nov 2014 - 16:41

score 391 · Answer 5 · 2014-11-23 19:40:28

391

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About images of (prime) ideals under injective endomorphisms

Published on 23 Nov 2014 - 19:40

score 2k · Answer 6 · 2014-11-23 20:34:12

2k

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Every ideal is contained in a prime ideal that is disjoint from a given multiplicative set

Published on 23 Nov 2014 - 20:34

score 699 · Answer 7 · 2014-11-24 00:08:30

699

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Quotient ring of the ring of integers of an algebraic number field and its fraction field

Published on 24 Nov 2014 - 0:08

score 115 · Answer 8 · 2014-11-24 16:50:30

115

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Factoring isomorphism

Published on 24 Nov 2014 - 16:50

score 3.5k · Answer 9 · 2014-11-24 19:04:48

3.5k

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$I$ is an ideal in $R$ implies that $I[x]$ is an ideal in $R[x]$.

Published on 24 Nov 2014 - 19:04

score 1.8k · Answer 10 · 2014-11-24 20:54:02

1.8k

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Comparing an ideal and its saturation

Published on 24 Nov 2014 - 20:54

score 1.5k · Answer 11 · 2014-11-24 22:23:44

1.5k

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Matrix rings and ideals

Published on 24 Nov 2014 - 22:23

score 997 · Answer 12 · 2026-03-28 03:16:13

997

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Questions about ring of smooth functions

Published on 28 Mar 2026 - 3:16

score 138 · Answer 13 · 2014-11-25 09:13:54

138

Views

Showing that an ideal is principal.

Published on 25 Nov 2014 - 9:13

score 209 · Answer 14 · 2026-03-28 13:21:58

209

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How to show that an ideal of $F[x]$ containing an irreducible polynomial of degree $n$ and a nonzero polynomial of degree $<n$ is $F[x]$?

Published on 28 Mar 2026 - 13:21

score 254 · Answer 15 · 2014-11-25 19:21:26

254

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Correspondence between ideals of $R$ and $D^{-1}R$

Published on 25 Nov 2014 - 19:21

List Question

Prime ideals of the ring of integers of an algebraic number field

Prove every prime ideal of a ring is a radical ideal.

Prove $\text{rad}(I)/I$ is isomorphic to $\mathfrak{N}(R/I)$

How to show that if $\gamma \alpha=0$ (mod $A$) then $\alpha = 0$ (mod $A$)

About images of (prime) ideals under injective endomorphisms

Every ideal is contained in a prime ideal that is disjoint from a given multiplicative set

Quotient ring of the ring of integers of an algebraic number field and its fraction field

Factoring isomorphism

$I$ is an ideal in $R$ implies that $I[x]$ is an ideal in $R[x]$.

Comparing an ideal and its saturation

Matrix rings and ideals

Questions about ring of smooth functions

Showing that an ideal is principal.

How to show that an ideal of $F[x]$ containing an irreducible polynomial of degree $n$ and a nonzero polynomial of degree $<n$ is $F[x]$?

Correspondence between ideals of $R$ and $D^{-1}R$

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