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Looking for a reference for this proof of radical ideals being finite intersections of prime ideals

score 151 · Answer 1 · 2018-04-27 11:28:18

151

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Looking for a reference for this proof of radical ideals being finite intersections of prime ideals

Published on 27 Apr 2018 - 11:28

score 1.1k · Answer 2 · 2018-04-29 05:02:00

1.1k

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The Jacobson radical of polynomial ring

Published on 29 Apr 2018 - 5:02

score 147 · Answer 3 · 2026-03-25 04:43:32

147

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$A = \langle p \rangle$ is a prime ideal of $\mathbb{Z}_n$ if and only if $p$ is a prime divisor of $n$

Published on 25 Mar 2026 - 4:43

score 282 · Answer 4 · 2018-05-03 09:54:30

282

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Prime Ideal Properly Contained in principal Ideal.

Published on 03 May 2018 - 9:54

score 283 · Answer 5 · 2018-05-05 10:02:23

283

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Simple commutative algebra localisation problem that I just can't seem to see

Published on 05 May 2018 - 10:02

score 918 · Answer 6 · 2026-03-25 08:12:37

918

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Prime ideal in valuation ring

Published on 25 Mar 2026 - 8:12

score 47 · Answer 7 · 2018-05-11 12:55:41

47

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Let $M$ be an irreducible $R$-module and $N$ be the order ideal of $m \in M$. Show that $N$ is maximal in $R_{R}$

Published on 11 May 2018 - 12:55

score 96 · Answer 8 · 2026-03-25 01:17:43

96

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Ideal generated by $x_1 - a_1, \dots, x_k - a_k$ is prime in polynomial ring over integral domain

Published on 25 Mar 2026 - 1:17

score 402 · Answer 9 · 2018-05-13 19:54:10

402

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prime ideals of $\mathbb{R}[X,Y]/(X-Y^2,X+Y)$

Published on 13 May 2018 - 19:54

score 70 · Answer 10 · 2026-03-25 07:45:47

70

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Let $R$ be a commutative ring with unity such that for some $n\ge 2$, $\prod_{1\le i <j\le n} (x_i-x_j)=0$ for every $x_1,...,x_n \in R$

Published on 25 Mar 2026 - 7:45

score 1.6k · Answer 11 · 2018-05-24 06:36:55

1.6k

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Number of maximal ideals of a commutative ring with unity which is not a field.

Published on 24 May 2018 - 6:36

score 332 · Answer 12 · 2018-05-24 14:17:21

332

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Prime ideal contains an integer

Published on 24 May 2018 - 14:17

score 537 · Answer 13 · 2018-05-25 12:29:54

537

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Semilocal ring with n maximal ideals?

Published on 25 May 2018 - 12:29

score 203 · Answer 14 · 2026-03-25 01:28:07

203

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Commutative, infinite, Noetherian ring with no non-trivial nilpotent and no non-trivial idempotent

Published on 25 Mar 2026 - 1:28

score 134 · Answer 15 · 2026-03-25 01:43:11

134

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Valuation ring whose unique maximal ideal and every ideal of finite height is principal

Published on 25 Mar 2026 - 1:43

List Question

Looking for a reference for this proof of radical ideals being finite intersections of prime ideals

The Jacobson radical of polynomial ring

$A = \langle p \rangle$ is a prime ideal of $\mathbb{Z}_n$ if and only if $p$ is a prime divisor of $n$

Prime Ideal Properly Contained in principal Ideal.

Simple commutative algebra localisation problem that I just can't seem to see

Prime ideal in valuation ring

Let $M$ be an irreducible $R$-module and $N$ be the order ideal of $m \in M$. Show that $N$ is maximal in $R_{R}$

Ideal generated by $x_1 - a_1, \dots, x_k - a_k$ is prime in polynomial ring over integral domain

prime ideals of $\mathbb{R}[X,Y]/(X-Y^2,X+Y)$

Let $R$ be a commutative ring with unity such that for some $n\ge 2$, $\prod_{1\le i <j\le n} (x_i-x_j)=0$ for every $x_1,...,x_n \in R$

Number of maximal ideals of a commutative ring with unity which is not a field.

Prime ideal contains an integer

Semilocal ring with n maximal ideals?

Commutative, infinite, Noetherian ring with no non-trivial nilpotent and no non-trivial idempotent

Valuation ring whose unique maximal ideal and every ideal of finite height is principal

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