Question

What does "under inclusion" mean in: $R$ is Noetherian ring $\iff$ Every nonempty set of ideals of $R$ contains a maximal element under inclusion.

score 287 · Answer 1 · 2018-12-21 10:45:29

What does "under inclusion" mean in: $R$ is Noetherian ring $\iff$ Every nonempty set of ideals of $R$ contains a maximal element under inclusion.

score 153 · Answer 2 · 2026-03-25 06:50:36

153

Views

$\mathcal{Nil}_n$ isomorphic to $h^A$ with $A=\mathbb{Z}[x]/(x^n)$

Published on 25 Mar 2026 - 6:50

score 206 · Answer 3 · 2026-03-25 06:51:36

206

Views

checking that there is a functor $\texttt{Nil}_n: Ring \longrightarrow Set$

Published on 25 Mar 2026 - 6:51

score 108 · Answer 4 · 2026-03-26 01:01:10

108

Views

Question regarding localization of polynomial ring

Published on 26 Mar 2026 - 1:01

score 67 · Answer 5 · 2018-12-23 01:07:17

67

Views

When $\mathbb{C}(f(t),g(t))=\mathbb{C}(t)$ implies that $\mathbb{C}[f(t),g(t)]=\mathbb{C}[t]$?

Published on 23 Dec 2018 - 1:07

score 381 · Answer 6 · 2026-03-25 05:09:44

381

Views

free resolution of $\mathbb{Z}$ as an $\mathbb{Z}[x]/(x^n-1)$-module

Published on 25 Mar 2026 - 5:09

score 292 · Answer 7 · 2026-04-03 19:43:58

292

Views

Quotient of annihilator ideal

Published on 03 Apr 2026 - 19:43

score 175 · Answer 8 · 2026-03-24 20:32:13

175

Views

Finding all primes above $x-a_i$ in the function field $y^2=(x-a_1)\cdots (x-a_n)$

Published on 24 Mar 2026 - 20:32

score 38 · Answer 9 · 2018-12-24 14:44:14

38

Views

how to show that $E(A,B_1\oplus B_2)\cong E(A,B_1)\times E(A,B_2)$

Published on 24 Dec 2018 - 14:44

score 200 · Answer 10 · 2026-03-26 09:11:24

200

Views

Existence and uniqueness of adjoints with respect to pairings

Published on 26 Mar 2026 - 9:11

score 417 · Answer 11 · 2018-12-21 16:14:25

417

Views

Is the integral closure of a polynomial ring a UFD?

Published on 21 Dec 2018 - 16:14

score 347 · Answer 12 · 2026-03-28 15:19:02

347

Views

Concerning the evaluation map

Published on 28 Mar 2026 - 15:19

score 341 · Answer 13 · 2026-03-28 15:26:49

341

Views

If spectrum of a commutative ring is empty

Published on 28 Mar 2026 - 15:26

score 1.1k · Answer 14 · 2026-03-28 16:56:26

1.1k

Views

Pullback of a Global Section

Published on 28 Mar 2026 - 16:56

score 54 · Answer 15 · 2026-04-03 21:05:18

54

Views

Show $A_{f(b)} \cong A \otimes _B B_g $

Published on 03 Apr 2026 - 21:05

List Question

What does "under inclusion" mean in: $R$ is Noetherian ring $\iff$ Every nonempty set of ideals of $R$ contains a maximal element under inclusion.

$\mathcal{Nil}_n$ isomorphic to $h^A$ with $A=\mathbb{Z}[x]/(x^n)$

checking that there is a functor $\texttt{Nil}_n: Ring \longrightarrow Set$

Question regarding localization of polynomial ring

When $\mathbb{C}(f(t),g(t))=\mathbb{C}(t)$ implies that $\mathbb{C}[f(t),g(t)]=\mathbb{C}[t]$?

free resolution of $\mathbb{Z}$ as an $\mathbb{Z}[x]/(x^n-1)$-module

Quotient of annihilator ideal

Finding all primes above $x-a_i$ in the function field $y^2=(x-a_1)\cdots (x-a_n)$

how to show that $E(A,B_1\oplus B_2)\cong E(A,B_1)\times E(A,B_2)$

Existence and uniqueness of adjoints with respect to pairings

Is the integral closure of a polynomial ring a UFD?

Concerning the evaluation map

If spectrum of a commutative ring is empty

Pullback of a Global Section

Show $A_{f(b)} \cong A \otimes _B B_g $

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