Question

A Nakayama like property implying certain ideal is in the Jacobson radical

score 187 · Answer 1 · 2017-08-03 17:47:13

187

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A Nakayama like property implying certain ideal is in the Jacobson radical

Published on 03 Aug 2017 - 17:47

score 54 · Answer 2 · 2026-03-28 12:15:49

54

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Minimal no. of generators of $mA_m$ , where $m$ is the maximal ideal $(\bar x -1 , \bar y -1)$ of $A=\mathbb C[x,y]/(x^3-y^2)$

Published on 28 Mar 2026 - 12:15

score 1.1k · Answer 3 · 2017-08-03 21:52:52

1.1k

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Slick proof the intersection of maximal ideals of a finitely generated domain is zero?

Published on 03 Aug 2017 - 21:52

score 106 · Answer 4 · 2026-03-28 12:14:33

106

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On simplifying $mR_m/m^2R_m$ where $m$ is maximal ideal of $R$

Published on 28 Mar 2026 - 12:14

score 182 · Answer 5 · 2017-08-07 09:21:12

182

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Is it true that every commutative ring with unity and finitely many maximal ideals can be written as finite direct product of local rings?

Published on 07 Aug 2017 - 9:21

score 341 · Answer 6 · 2026-03-28 15:20:16

341

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Does the strong form of Hilbert Nullstellensatz say how the maximal ideals look like?

Published on 28 Mar 2026 - 15:20

score 932 · Answer 7 · 2017-08-08 18:28:03

932

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Primideal, maximal ideal, $\mathbb{Z}[\sqrt{3}]$

Published on 08 Aug 2017 - 18:28

score 92 · Answer 8 · 2017-08-15 07:32:26

92

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A question on algebraically closed field

Published on 15 Aug 2017 - 7:32

score 510 · Answer 9 · 2017-08-15 15:23:43

510

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Let $R$ be a commutative ring and $I $ be a maximal ideal of $R$. Then $I$ is a radical ideal of $R$

Published on 15 Aug 2017 - 15:23

score 232 · Answer 10 · 2017-08-15 23:29:13

232

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Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.

Published on 15 Aug 2017 - 23:29

score 565 · Answer 11 · 2017-08-20 17:54:46

565

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If $I$ is not finitely generated and every ideal properly containing $I$ is finitely generated, then $I$ is prime?

Published on 20 Aug 2017 - 17:54

score 149 · Answer 12 · 2017-08-22 05:30:23

149

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Identification of Quotient Rings

Published on 22 Aug 2017 - 5:30

score 89 · Answer 13 · 2026-03-27 00:04:01

89

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Finding an explicit isomorphism between $\mathbb{C}_q[x^{\pm 1},y^{\pm 1}]/\langle x^k-\alpha, y^k-\beta \rangle$ and $M_k(\mathbb{C})$

Published on 27 Mar 2026 - 0:04

score 3k · Answer 14 · 2017-08-24 16:16:16

3k

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$(X^2-Y^3)$ is prime ideal in $K[X,Y]$

Published on 24 Aug 2017 - 16:16

score 576 · Answer 15 · 2017-08-24 17:57:57

576

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Prime avoidance lemma of E. Davis [Exercise 16.8 in Matsumura, Commutative Ring Theory, related with finite union of prime ideals]

Published on 24 Aug 2017 - 17:57

List Question

A Nakayama like property implying certain ideal is in the Jacobson radical

Minimal no. of generators of $mA_m$ , where $m$ is the maximal ideal $(\bar x -1 , \bar y -1)$ of $A=\mathbb C[x,y]/(x^3-y^2)$

Slick proof the intersection of maximal ideals of a finitely generated domain is zero?

On simplifying $mR_m/m^2R_m$ where $m$ is maximal ideal of $R$

Is it true that every commutative ring with unity and finitely many maximal ideals can be written as finite direct product of local rings?

Does the strong form of Hilbert Nullstellensatz say how the maximal ideals look like?

Primideal, maximal ideal, $\mathbb{Z}[\sqrt{3}]$

A question on algebraically closed field

Let $R$ be a commutative ring and $I $ be a maximal ideal of $R$. Then $I$ is a radical ideal of $R$

Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.

If $I$ is not finitely generated and every ideal properly containing $I$ is finitely generated, then $I$ is prime?

Identification of Quotient Rings

Finding an explicit isomorphism between $\mathbb{C}_q[x^{\pm 1},y^{\pm 1}]/\langle x^k-\alpha, y^k-\beta \rangle$ and $M_k(\mathbb{C})$

$(X^2-Y^3)$ is prime ideal in $K[X,Y]$

Prime avoidance lemma of E. Davis [Exercise 16.8 in Matsumura, Commutative Ring Theory, related with finite union of prime ideals]

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