Question

In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?

score 329 · Answer 1 · 2026-05-07 13:38:16

329

Views

In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?

Published on 07 May 2026 - 13:38

score 1.5k · Answer 2 · 2026-05-07 12:46:55

1.5k

Views

Prove that the field $k(x)$ of rational functions over $k$ in the variable $x$ is not a finitely generated $k$-algebra.

Published on 07 May 2026 - 12:46

score 185 · Answer 3 · 2026-05-07 18:00:43

185

Views

Ascending chain of proper submodules in a module all whose proper submodules are Noetherian

Published on 07 May 2026 - 18:00

score 529 · Answer 4 · 2026-04-29 12:43:06

529

Views

Noetherian local domain of dimension one

Published on 29 Apr 2026 - 12:43

score 310 · Answer 5 · 2026-04-29 12:42:49

310

Views

Dimension of Quotient of Noetherian local ring

Published on 29 Apr 2026 - 12:42

score 525 · Answer 6 · 2026-05-06 10:02:35

525

Views

Is $\mathbb{Z}[\frac{1}{2}]$ Noetherian?

Published on 06 May 2026 - 10:02

score 578 · Answer 7 · 2026-04-29 12:25:52

578

Views

Finitely generated modules over noetherian rings

Published on 29 Apr 2026 - 12:25

score 111 · Answer 8 · 2026-04-29 12:42:49

111

Views

Simplicity of Noetherian $B$, $A \subseteq B\subseteq C$, where $A$ and $C$ are simple Noetherian domains

Published on 29 Apr 2026 - 12:42

score 1.6k · Answer 9 · 2026-04-29 12:42:52

1.6k

Views

Why noetherian ring satisfies the maximal condition?

Published on 29 Apr 2026 - 12:42

score 486 · Answer 10 · 2026-05-06 07:33:29

486

Views

If M is a a left module over $M_n(D)$ where $D$ is a division ring, M is Noetherian iff Artinian

Published on 06 May 2026 - 7:33

score 247 · Answer 11 · 2026-04-29 12:42:49

247

Views

torsion-free modules $M$ over Noetherian domain of dimension $1$ for which $l(M/aM) \le (\dim_K K \otimes_R M) \cdot l(R/aR), \forall 0 \ne a \in R$

Published on 29 Apr 2026 - 12:42

score 805 · Answer 12 · 2026-05-10 16:11:26

805

Views

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Published on 10 May 2026 - 16:11

score 202 · Answer 13 · 2026-05-03 07:32:36

202

Views

Checking if quotient ring is Noetherian or Artinian over a module

Published on 03 May 2026 - 7:32

score 173 · Answer 14 · 2026-04-29 12:42:50

173

Views

Associated primes to principal ideals in a Noetherian domain

Published on 29 Apr 2026 - 12:42

score 445 · Answer 15 · 2026-05-10 12:32:06

445

Views

Commutative Noetherian prime ideals finitely generated

Published on 10 May 2026 - 12:32

List Question

In a left noetherian ring, does having a left inverse for an element guarantee the existence of right inverse for that element?

Prove that the field $k(x)$ of rational functions over $k$ in the variable $x$ is not a finitely generated $k$-algebra.

Ascending chain of proper submodules in a module all whose proper submodules are Noetherian

Noetherian local domain of dimension one

Dimension of Quotient of Noetherian local ring

Is $\mathbb{Z}[\frac{1}{2}]$ Noetherian?

Finitely generated modules over noetherian rings

Simplicity of Noetherian $B$, $A \subseteq B\subseteq C$, where $A$ and $C$ are simple Noetherian domains

Why noetherian ring satisfies the maximal condition?

If M is a a left module over $M_n(D)$ where $D$ is a division ring, M is Noetherian iff Artinian

torsion-free modules $M$ over Noetherian domain of dimension $1$ for which $l(M/aM) \le (\dim_K K \otimes_R M) \cdot l(R/aR), \forall 0 \ne a \in R$

Commutative Noetherian, local, reduced ring has only one minimal prime ideal?

Checking if quotient ring is Noetherian or Artinian over a module

Associated primes to principal ideals in a Noetherian domain

Commutative Noetherian prime ideals finitely generated

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