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Question on proof : $I\leq R$ is an ideal s.t. $\sqrt I$ is maximal, then $I$ is primary.

score 664 · Answer 1 · 2017-01-29 10:54:14

664

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Question on proof : $I\leq R$ is an ideal s.t. $\sqrt I$ is maximal, then $I$ is primary.

Published on 29 Jan 2017 - 10:54

score 271 · Answer 2 · 2017-01-29 15:04:40

271

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Radical of ideal

Published on 29 Jan 2017 - 15:04

score 7.4k · Answer 3 · 2017-01-29 22:22:27

7.4k

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Why principal ideals in Z[x] are not maximal?

Published on 29 Jan 2017 - 22:22

score 309 · Answer 4 · 2017-01-31 01:47:22

309

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Prove that any ideal of $R$ containing $1$ must be $R$

Published on 31 Jan 2017 - 1:47

score 4.3k · Answer 5 · 2017-01-31 11:37:47

Let $A$ and $B$ be two ideals of a commutative ring $R$ with unity such that $A+B=R$. Show that $AB = A \cap B$

score 62 · Answer 6 · 2017-01-31 16:20:30

62

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Ideal in a polynomial ring quesiton

Published on 31 Jan 2017 - 16:20

score 136 · Answer 7 · 2017-02-01 03:26:05

136

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Associated prime ideal of the ring $C([0,1])$

Published on 01 Feb 2017 - 3:26

score 1.8k · Answer 8 · 2017-02-01 17:51:10

1.8k

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How I have to imagine the quotient ring $\mathbb{Z}[x]/(nx)$?

Published on 01 Feb 2017 - 17:51

score 851 · Answer 9 · 2026-03-26 16:10:17

851

Views

Let $R$ be an integral domain and $I,J$ be ideals such that $IJ$ is a principal ideal. Then $I$ is finitely generated?

Published on 26 Mar 2026 - 16:10

score 78 · Answer 10 · 2017-02-02 20:40:36

$\phi:R\to S$ is a ring homomorphism and $I\subset S$ is an ideal, then $\phi$ induces an injection $R/(\phi^{-1}(I))\subset S/I$.

score 544 · Answer 11 · 2026-03-26 06:29:11

544

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If $S=R/Nil(R)$ is a quotient ring then $Nil(S)=\{0_s\}$

Published on 26 Mar 2026 - 6:29

score 59 · Answer 12 · 2026-03-25 08:13:37

59

Views

Show that if $f_1(1+xy+x^4)+f_2(y^2+x-1)+f_3(xy-1)=1$ in $k[x,y]$ no $f_i$ can be a nonzero element of $k$.

Published on 25 Mar 2026 - 8:13

score 48 · Answer 13 · 2017-02-03 20:32:13

48

Views

Is it possible for an ideal and its dual filter to have common members?

Published on 03 Feb 2017 - 20:32

score 2k · Answer 14 · 2017-02-04 16:07:16

2k

Views

Principal ideal $(a) = R$ iff $a$ is a unit

Published on 04 Feb 2017 - 16:07

score 652 · Answer 15 · 2026-04-01 10:31:03

652

Views

Gcd between Ideals

Published on 01 Apr 2026 - 10:31

List Question

Question on proof : $I\leq R$ is an ideal s.t. $\sqrt I$ is maximal, then $I$ is primary.

Radical of ideal

Why principal ideals in Z[x] are not maximal?

Prove that any ideal of $R$ containing $1$ must be $R$

Let $A$ and $B$ be two ideals of a commutative ring $R$ with unity such that $A+B=R$. Show that $AB = A \cap B$

Ideal in a polynomial ring quesiton

Associated prime ideal of the ring $C([0,1])$

How I have to imagine the quotient ring $\mathbb{Z}[x]/(nx)$?

Let $R$ be an integral domain and $I,J$ be ideals such that $IJ$ is a principal ideal. Then $I$ is finitely generated?

$\phi:R\to S$ is a ring homomorphism and $I\subset S$ is an ideal, then $\phi$ induces an injection $R/(\phi^{-1}(I))\subset S/I$.

If $S=R/Nil(R)$ is a quotient ring then $Nil(S)=\{0_s\}$

Show that if $f_1(1+xy+x^4)+f_2(y^2+x-1)+f_3(xy-1)=1$ in $k[x,y]$ no $f_i$ can be a nonzero element of $k$.

Is it possible for an ideal and its dual filter to have common members?

Principal ideal $(a) = R$ iff $a$ is a unit

Gcd between Ideals

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