Question

In $\mathbb Z[x]$, is $(2,x)=(2)+(x)$?

score 46 · Answer 1 · 2019-06-09 07:48:59

46

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In $\mathbb Z[x]$, is $(2,x)=(2)+(x)$?

Published on 09 Jun 2019 - 7:48

score 1.4k · Answer 2 · 2026-03-25 21:14:12

1.4k

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$(0)$ and $p^n\mathbb{Z}$ (where $p$ prime, $n$ positive integer) are the only primary ideals in $\mathbb{Z}$

Published on 25 Mar 2026 - 21:14

score 139 · Answer 3 · 2026-03-25 17:18:21

139

Views

why is a ring ideal not called a filter

Published on 25 Mar 2026 - 17:18

score 62 · Answer 4 · 2019-06-12 16:59:14

62

Views

$\mathfrak{q}$ is primary iff: given $a,b \in A$, $ab \in \mathfrak{q}$ and $a \not\in \mathfrak{q}$, then $b^n \in \mathfrak{q}$ for some $n \geq 1$

Published on 12 Jun 2019 - 16:59

score 194 · Answer 5 · 2026-03-25 15:42:25

194

Views

Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

Published on 25 Mar 2026 - 15:42

score 61 · Answer 6 · 2026-03-27 20:27:27

61

Views

show that a kernel is principal, here the application : $ \text{ev}_{x = t^2, y = t^3} $

Published on 27 Mar 2026 - 20:27

score 44 · Answer 7 · 2019-06-14 10:31:08

44

Views

Prove that $\left( I_1I_2 \right)^e=I_1^e I_2^e$

Published on 14 Jun 2019 - 10:31

score 259 · Answer 8 · 2026-03-27 13:47:25

259

Views

Decomposition of semi-simple Lie algebra into simple lie algebra (or ideal?)

Published on 27 Mar 2026 - 13:47

score 34 · Answer 9 · 2019-06-15 08:29:46

34

Views

For ideals of $R$, $I_1, I_2$, Is it true that $(I_1 \cap I_2)M \cong I_1 M \cap I_2 M$ for any $R$-module $M$?

Published on 15 Jun 2019 - 8:29

score 271 · Answer 10 · 2026-03-25 10:55:58

271

Views

Inverse of a finitely generated ideal in UFD

Published on 25 Mar 2026 - 10:55

score 493 · Answer 11 · 2026-03-25 12:27:06

493

Views

Find an ideal $I$ in $A$ so that $A/I$ is a finite field with $25$ elements.

Published on 25 Mar 2026 - 12:27

score 331 · Answer 12 · 2026-03-25 13:53:38

331

Views

Understanding the Definition of Ideals Generated by Polynomials

Published on 25 Mar 2026 - 13:53

score 64 · Answer 13 · 2026-03-25 18:46:37

64

Views

Lemma for Chinese Remainder Theorem

Published on 25 Mar 2026 - 18:46

score 36 · Answer 14 · 2019-06-18 09:19:20

36

Views

How do you prove that 2 nontrivial ideals are the only nontrivial ideals in a ring?

Published on 18 Jun 2019 - 9:19

score 154 · Answer 15 · 2026-03-29 15:33:02

154

Views

Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

Published on 29 Mar 2026 - 15:33

List Question

In $\mathbb Z[x]$, is $(2,x)=(2)+(x)$?

$(0)$ and $p^n\mathbb{Z}$ (where $p$ prime, $n$ positive integer) are the only primary ideals in $\mathbb{Z}$

why is a ring ideal not called a filter

$\mathfrak{q}$ is primary iff: given $a,b \in A$, $ab \in \mathfrak{q}$ and $a \not\in \mathfrak{q}$, then $b^n \in \mathfrak{q}$ for some $n \geq 1$

Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

show that a kernel is principal, here the application : $ \text{ev}_{x = t^2, y = t^3} $

Prove that $\left( I_1I_2 \right)^e=I_1^e I_2^e$

Decomposition of semi-simple Lie algebra into simple lie algebra (or ideal?)

For ideals of $R$, $I_1, I_2$, Is it true that $(I_1 \cap I_2)M \cong I_1 M \cap I_2 M$ for any $R$-module $M$?

Inverse of a finitely generated ideal in UFD

Find an ideal $I$ in $A$ so that $A/I$ is a finite field with $25$ elements.

Understanding the Definition of Ideals Generated by Polynomials

Lemma for Chinese Remainder Theorem

How do you prove that 2 nontrivial ideals are the only nontrivial ideals in a ring?

Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

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