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

score 154 · Answer 1 · 2026-04-12 17:10:16

154

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

Published on 12 Apr 2026 - 17:10

score 1.1k · Answer 2 · 2026-04-16 21:22:37

1.1k

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The Jacobson radical of polynomial ring

Published on 16 Apr 2026 - 21:22

score 150 · Answer 3 · 2026-05-10 12:35:32

150

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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 10 May 2026 - 12:35

score 285 · Answer 4 · 2026-04-12 09:47:25

285

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Prime Ideal Properly Contained in principal Ideal.

Published on 12 Apr 2026 - 9:47

score 287 · Answer 5 · 2026-05-10 15:28:53

287

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

Published on 10 May 2026 - 15:28

score 923 · Answer 6 · 2026-05-10 12:43:14

923

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Prime ideal in valuation ring

Published on 10 May 2026 - 12:43

score 49 · Answer 7 · 2026-04-18 12:55:33

49

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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 18 Apr 2026 - 12:55

score 99 · Answer 8 · 2026-05-10 12:34:50

99

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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 10 May 2026 - 12:34

score 404 · Answer 9 · 2026-04-15 13:31:48

404

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

Published on 15 Apr 2026 - 13:31

score 73 · Answer 10 · 2026-05-10 13:51:09

73

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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 10 May 2026 - 13:51

score 1.6k · Answer 11 · 2026-04-13 02:59:44

1.6k

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

Published on 13 Apr 2026 - 2:59

score 336 · Answer 12 · 2026-04-11 22:13:21

336

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Prime ideal contains an integer

Published on 11 Apr 2026 - 22:13

score 540 · Answer 13 · 2026-04-14 09:48:53

540

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Semilocal ring with n maximal ideals?

Published on 14 Apr 2026 - 9:48

score 206 · Answer 14 · 2026-05-10 13:50:32

206

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

Published on 10 May 2026 - 13:50

score 140 · Answer 15 · 2026-05-10 12:34:59

140

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

Published on 10 May 2026 - 12:34

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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