Question

$I=(3,x^2+1)$ be an ideal of $\mathbb{Z}[x]$. Then $I$ is a proper ideal of $\mathbb{Z}[x]$

score 2k · Answer 1 · 2026-04-12 20:51:03

2k

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$I=(3,x^2+1)$ be an ideal of $\mathbb{Z}[x]$. Then $I$ is a proper ideal of $\mathbb{Z}[x]$

Published on 12 Apr 2026 - 20:51

score 213 · Answer 2 · 2026-04-15 13:19:02

213

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$I$ semisimple + $R/I$ semisimple $\implies$ $R$ semisimple

Published on 15 Apr 2026 - 13:19

score 340 · Answer 3 · 2026-04-15 19:49:52

340

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If $Q$ is P-primary, then $Q/I$ is $P/I$-primary

Published on 15 Apr 2026 - 19:49

score 1.5k · Answer 4 · 2026-04-15 16:16:17

1.5k

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If every ascending chain of primary ideals in $R$ stabilizes, is $R$ a Noetherian ring?

Published on 15 Apr 2026 - 16:16

score 458 · Answer 5 · 2026-04-13 09:04:39

458

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Ascending chain "stabilizing temporarily" infinitely many times

Published on 13 Apr 2026 - 9:04

score 152 · Answer 6 · 2026-04-12 01:59:29

152

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Why is closeness of an ideal useful?

Published on 12 Apr 2026 - 1:59

score 383 · Answer 7 · 2026-04-16 22:12:46

383

Views

Why is the Noetherian hypothesis necessary for this fact about associated primes?

Published on 16 Apr 2026 - 22:12

score 637 · Answer 8 · 2026-04-05 22:16:52

637

Views

Prime ideals and epimorphism

Published on 05 Apr 2026 - 22:16

score 63 · Answer 9 · 2026-04-11 13:18:36

63

Views

A question on generators

Published on 11 Apr 2026 - 13:18

score 100 · Answer 10 · 2026-04-14 04:23:01

100

Views

Ideals in ring extensions

Published on 14 Apr 2026 - 4:23

score 104 · Answer 11 · 2026-04-13 23:31:08

104

Views

Kronecker's approach to unique factorisation in algebraic number theory: books and references

Published on 13 Apr 2026 - 23:31

score 478 · Answer 12 · 2026-04-11 14:44:56

478

Views

An ideal in the ring of infinitely differentiable functions

Published on 11 Apr 2026 - 14:44

score 339 · Answer 13 · 2026-04-15 21:26:17

339

Views

Reading multiplicity of cusps , singularity etc from initial polynomial.

Published on 15 Apr 2026 - 21:26

score 293 · Answer 14 · 2026-04-14 13:13:30

293

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Non Classical Examples of Indecomposable Ideals

Published on 14 Apr 2026 - 13:13

score 314 · Answer 15 · 2026-04-15 04:44:20

314

Views

Isomorphic factor rings of polynomial rings does imply isomorphic ideals?

Published on 15 Apr 2026 - 4:44

List Question

$I=(3,x^2+1)$ be an ideal of $\mathbb{Z}[x]$. Then $I$ is a proper ideal of $\mathbb{Z}[x]$

$I$ semisimple + $R/I$ semisimple $\implies$ $R$ semisimple

If $Q$ is P-primary, then $Q/I$ is $P/I$-primary

If every ascending chain of primary ideals in $R$ stabilizes, is $R$ a Noetherian ring?

Ascending chain "stabilizing temporarily" infinitely many times

Why is closeness of an ideal useful?

Why is the Noetherian hypothesis necessary for this fact about associated primes?

Prime ideals and epimorphism

A question on generators

Ideals in ring extensions

Kronecker's approach to unique factorisation in algebraic number theory: books and references

An ideal in the ring of infinitely differentiable functions

Reading multiplicity of cusps , singularity etc from initial polynomial.

Non Classical Examples of Indecomposable Ideals

Isomorphic factor rings of polynomial rings does imply isomorphic ideals?

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