Question

Initial object in category of rings (with unity)

score 2.4k · Answer 1 · 2026-04-04 03:58:10

2.4k

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Initial object in category of rings (with unity)

Published on 04 Apr 2026 - 3:58

score 899 · Answer 2 · 2026-03-26 20:41:12

899

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Why is $(X^5-1)/(X-1)$ the minimal polynomial for $e^{2\pi i/5}$, the fifth root of unity, over $\Bbb Q$?

Published on 26 Mar 2026 - 20:41

score 93 · Answer 3 · 2026-03-25 13:54:43

93

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Two Sided Ideal in Left-Localization of a Left-Noetherian Ring

Published on 25 Mar 2026 - 13:54

score 388 · Answer 4 · 2026-03-28 14:19:36

388

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Is it true that no polynomial (with the exception of constant polynomial) have an inverse in $\mathbb Z/p\mathbb Z$ (where p is prime)?

Published on 28 Mar 2026 - 14:19

score 974 · Answer 5 · 2026-03-26 20:38:16

974

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polynomial units in field

Published on 26 Mar 2026 - 20:38

score 52 · Answer 6 · 2026-03-25 03:03:46

52

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Given a $k$ algebra $A_0$, find another $k$ algebra $A$ with identity such that the extension $A_0\subseteq A$ has dimension $1$.

Published on 25 Mar 2026 - 3:03

score 228 · Answer 7 · 2026-04-05 11:02:13

228

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Confusion over Socle

Published on 05 Apr 2026 - 11:02

score 71 · Answer 8 · 2026-03-25 13:58:00

71

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Grillet's "Abstract Algebra", p. 148, ex. 3: Noetherian subring of a ring

Published on 25 Mar 2026 - 13:58

score 2.6k · Answer 9 · 2019-04-02 22:18:37

2.6k

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Show that $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$

Published on 02 Apr 2019 - 22:18

score 81 · Answer 10 · 2026-04-06 09:24:26

81

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How does the product $q_j X^j_m$ make sense in this context?

Published on 06 Apr 2026 - 9:24

score 142 · Answer 11 · 2026-03-25 14:27:24

142

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Fraction field of $A[[t]]$

Published on 25 Mar 2026 - 14:27

score 178 · Answer 12 · 2019-04-03 16:14:44

178

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If $i:R \rightarrow S$ is an injective, non-surjective ring homomorphism, then $R \simeq S$?

Published on 03 Apr 2019 - 16:14

score 219 · Answer 13 · 2026-03-31 21:13:39

219

Views

Prove that $\mathbb{Q}(\sqrt{-3})=\mathbb{Q}(\omega)$

Published on 31 Mar 2026 - 21:13

score 514 · Answer 14 · 2026-03-25 13:54:13

514

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Noetherian ring has an associated prime ideal

Published on 25 Mar 2026 - 13:54

score 234 · Answer 15 · 2026-03-25 13:56:47

234

Views

Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

Published on 25 Mar 2026 - 13:56

List Question

Initial object in category of rings (with unity)

Why is $(X^5-1)/(X-1)$ the minimal polynomial for $e^{2\pi i/5}$, the fifth root of unity, over $\Bbb Q$?

Two Sided Ideal in Left-Localization of a Left-Noetherian Ring

Is it true that no polynomial (with the exception of constant polynomial) have an inverse in $\mathbb Z/p\mathbb Z$ (where p is prime)?

polynomial units in field

Given a $k$ algebra $A_0$, find another $k$ algebra $A$ with identity such that the extension $A_0\subseteq A$ has dimension $1$.

Confusion over Socle

Grillet's "Abstract Algebra", p. 148, ex. 3: Noetherian subring of a ring

Show that $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$

How does the product $q_j X^j_m$ make sense in this context?

Fraction field of $A[[t]]$

If $i:R \rightarrow S$ is an injective, non-surjective ring homomorphism, then $R \simeq S$?

Prove that $\mathbb{Q}(\sqrt{-3})=\mathbb{Q}(\omega)$

Noetherian ring has an associated prime ideal

Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

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