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 251 · Answer 2 · 2026-03-22 00:09:30

251

Views

Ring of remainders definition

Published on 22 Mar 2026 - 0:09

score 254 · Answer 3 · 2026-03-17 15:23:37

254

Views

$[Solved]$ Find all units in the ring $M_2(\mathbb{Z})$

Published on 17 Mar 2026 - 15:23

score 88 · Answer 4 · 2026-03-17 22:17:43

88

Views

$[Solved]$ Write polynomial as a product of irreducible elements

Published on 17 Mar 2026 - 22:17

score 50 · Answer 5 · 2018-01-16 16:20:19

50

Views

For a surjective function $f: A \rightarrow A$, if there exist $n$ such that $\ker f^n = \ker f^{n+1} = \dots$ Is f injective?

Published on 16 Jan 2018 - 16:20

score 1k · Answer 6 · 2026-03-22 07:10:50

1k

Views

Jacobson radical of formal power series over an integral domain

Published on 22 Mar 2026 - 7:10

score 77 · Answer 7 · 2026-03-17 04:30:24

77

Views

The amount of elements in a quotient ring

Published on 17 Mar 2026 - 4:30

score 576 · Answer 8 · 2026-03-17 10:11:30

576

Views

Identify $\mathbb{Z}[x]/(x^2-3,2x+4)$.

Published on 17 Mar 2026 - 10:11

score 1.5k · Answer 9 · 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 104 · Answer 10 · 2018-01-17 10:18:51

Let $R$ be a commutative ring with unit. Show that $\langle a\rangle = \langle b\rangle \iff a$ and $b$ are friends

score 178 · Answer 11 · 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 640 · Answer 12 · 2026-03-17 03:09:42

640

Views

$1+i$ is prime in $\mathbb Z[i]$

Published on 17 Mar 2026 - 3:09

score 114 · Answer 13 · 2026-03-17 23:20:38

114

Views

A question on the group algebra

Published on 17 Mar 2026 - 23:20

score 367 · Answer 14 · 2026-03-17 12:12:58

367

Views

The radical of the algebra $ A = T_n(F)$ is $N$, the set of all strictly upper triangular matrices.

Published on 17 Mar 2026 - 12:12

score 612 · Answer 15 · 2026-03-22 17:50:43

612

Views

Primary ideals in an Artinial local ring

Published on 22 Mar 2026 - 17:50

List Question

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

Ring of remainders definition

$[Solved]$ Find all units in the ring $M_2(\mathbb{Z})$

$[Solved]$ Write polynomial as a product of irreducible elements

For a surjective function $f: A \rightarrow A$, if there exist $n$ such that $\ker f^n = \ker f^{n+1} = \dots$ Is f injective?

Jacobson radical of formal power series over an integral domain

The amount of elements in a quotient ring

Identify $\mathbb{Z}[x]/(x^2-3,2x+4)$.

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

Let $R$ be a commutative ring with unit. Show that $\langle a\rangle = \langle b\rangle \iff a$ and $b$ are friends

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

$1+i$ is prime in $\mathbb Z[i]$

A question on the group algebra

The radical of the algebra $ A = T_n(F)$ is $N$, the set of all strictly upper triangular matrices.

Primary ideals in an Artinial local ring

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