Question

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

score 320 · Answer 1 · 2026-03-24 10:15:48

320

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 24 Mar 2026 - 10:15

score 1.5k · Answer 2 · 2026-03-19 20:24:25

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 19 Mar 2026 - 20:24

score 178 · Answer 3 · 2026-03-20 10:16:30

178

Views

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

Published on 20 Mar 2026 - 10:16

score 521 · Answer 4 · 2026-03-20 03:15:51

521

Views

Noetherian local domain of dimension one

Published on 20 Mar 2026 - 3:15

score 304 · Answer 5 · 2026-03-20 23:10:59

304

Views

Dimension of Quotient of Noetherian local ring

Published on 20 Mar 2026 - 23:10

score 517 · Answer 6 · 2026-03-22 05:07:25

517

Views

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

Published on 22 Mar 2026 - 5:07

score 571 · Answer 7 · 2026-03-23 00:41:01

571

Views

Finitely generated modules over noetherian rings

Published on 23 Mar 2026 - 0:41

score 103 · Answer 8 · 2026-03-20 06:50:51

103

Views

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

Published on 20 Mar 2026 - 6:50

score 1.6k · Answer 9 · 2026-03-22 04:22:26

1.6k

Views

Why noetherian ring satisfies the maximal condition?

Published on 22 Mar 2026 - 4:22

score 478 · Answer 10 · 2026-03-22 04:54:29

478

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 22 Mar 2026 - 4:54

score 239 · Answer 11 · 2026-03-23 03:17:17

239

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 23 Mar 2026 - 3:17

score 793 · Answer 12 · 2026-03-22 17:31:00

793

Views

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

Published on 22 Mar 2026 - 17:31

score 195 · Answer 13 · 2026-03-22 17:24:19

195

Views

Checking if quotient ring is Noetherian or Artinian over a module

Published on 22 Mar 2026 - 17:24

score 166 · Answer 14 · 2026-03-19 23:41:27

166

Views

Associated primes to principal ideals in a Noetherian domain

Published on 19 Mar 2026 - 23:41

score 435 · Answer 15 · 2026-03-17 18:53:38

435

Views

Commutative Noetherian prime ideals finitely generated

Published on 17 Mar 2026 - 18:53

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

Trending Questions

Popular # Hahtags

Popular Questions