Question

$R/\langle p^k\rangle$ is an associator (i.e. if $\langle a\rangle = \langle b\rangle,$ then $a$ and $b$ are associates) when $R$ is a PID.

score 119 · Answer 1 · 2026-04-13 12:21:13

119

Views

$R/\langle p^k\rangle$ is an associator (i.e. if $\langle a\rangle = \langle b\rangle,$ then $a$ and $b$ are associates) when $R$ is a PID.

Published on 13 Apr 2026 - 12:21

score 1.2k · Answer 2 · 2026-04-14 03:23:09

1.2k

Views

Why $\langle x^2+1\rangle$ is not prime in $\mathbb{Z}_2[x]$?

Published on 14 Apr 2026 - 3:23

score 52 · Answer 3 · 2026-04-12 10:57:37

52

Views

Showing an isomorphism of rings

Published on 12 Apr 2026 - 10:57

score 671 · Answer 4 · 2026-04-16 06:52:54

671

Views

$I$ is the maximal left ideal

Published on 16 Apr 2026 - 6:52

score 303 · Answer 5 · 2026-04-11 23:58:04

303

Views

$17\mathbb{Z}[\sqrt {10}]$ is prime ideal in $\mathbb{Z}[\sqrt {10}]$

Published on 11 Apr 2026 - 23:58

score 110 · Answer 6 · 2026-04-10 06:20:41

110

Views

How to decompose an ideal as intersection of simpler ideals?

Published on 10 Apr 2026 - 6:20

score 229 · Answer 7 · 2026-03-26 22:16:08

229

Views

A homogeneous principal prime ideal in $K[x_1,\dots,x_n]$ is generated by a homogeneous element.

Published on 26 Mar 2026 - 22:16

score 57 · Answer 8 · 2026-04-12 14:46:19

57

Views

How are varieties related polynomials?

Published on 12 Apr 2026 - 14:46

score 244 · Answer 9 · 2026-04-11 05:16:12

244

Views

A prime ideal which is not maximal

Published on 11 Apr 2026 - 5:16

score 113 · Answer 10 · 2026-04-15 15:50:24

113

Views

Showing that $\mathrm{Rad}((0)) ≠ (0)$ implies $R^\times \subsetneq R[X]^\times$

Published on 15 Apr 2026 - 15:50

score 444 · Answer 11 · 2026-04-10 00:07:19

444

Views

How do I find the ideal $I+J$ and quotient $R/(I+J)$?

Published on 10 Apr 2026 - 0:07

score 75 · Answer 12 · 2026-03-25 07:42:01

75

Views

Relationship between ST-Path Ideals and ST-Cut Ideals?

Published on 25 Mar 2026 - 7:42

score 153 · Answer 13 · 2026-04-14 07:40:15

153

Views

Principal ideal of $\mathbb{C}[Z,\bar{Z}]$

Published on 14 Apr 2026 - 7:40

score 518 · Answer 14 · 2026-04-14 11:08:58

518

Views

Finding nilpotent elements in a quotient ring.

Published on 14 Apr 2026 - 11:08

score 1.1k · Answer 15 · 2026-04-12 13:20:39

1.1k

Views

When a prime ideal in polynomial ring over integers is principal

Published on 12 Apr 2026 - 13:20

List Question

$R/\langle p^k\rangle$ is an associator (i.e. if $\langle a\rangle = \langle b\rangle,$ then $a$ and $b$ are associates) when $R$ is a PID.

Why $\langle x^2+1\rangle$ is not prime in $\mathbb{Z}_2[x]$?

Showing an isomorphism of rings

$I$ is the maximal left ideal

$17\mathbb{Z}[\sqrt {10}]$ is prime ideal in $\mathbb{Z}[\sqrt {10}]$

How to decompose an ideal as intersection of simpler ideals?

A homogeneous principal prime ideal in $K[x_1,\dots,x_n]$ is generated by a homogeneous element.

How are varieties related polynomials?

A prime ideal which is not maximal

Showing that $\mathrm{Rad}((0)) ≠ (0)$ implies $R^\times \subsetneq R[X]^\times$

How do I find the ideal $I+J$ and quotient $R/(I+J)$?

Relationship between ST-Path Ideals and ST-Cut Ideals?

Principal ideal of $\mathbb{C}[Z,\bar{Z}]$

Finding nilpotent elements in a quotient ring.

When a prime ideal in polynomial ring over integers is principal

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