Question

How should one interpret $R[A_1,..,A_n]$ where $R$ is a unital ring and $A_i\in M_{n\times n}(R)$

score 38 · Answer 1 · 2020-03-23 13:23:02

38

Views

How should one interpret $R[A_1,..,A_n]$ where $R$ is a unital ring and $A_i\in M_{n\times n}(R)$

Published on 23 Mar 2020 - 13:23

score 157 · Answer 2 · 2026-02-23 03:57:10

157

Views

Number of maximal subgroups in finitely generated amenable groups

Published on 23 Feb 2026 - 3:57

score 147 · Answer 3 · 2020-03-24 11:06:51

147

Views

Can a quotient of a polynomial ring by $n-1$ polynomials make $n$ variables $m$th powers?

Published on 24 Mar 2020 - 11:06

score 426 · Answer 4 · 2026-03-25 18:53:52

426

Views

Torsion in finitely generated modules over polynomial rings

Published on 25 Mar 2026 - 18:53

score 64 · Answer 5 · 2020-03-25 10:20:08

64

Views

If $\{e_1,...,e_n\}$ is a $\Bbb Z$-basis of $\Bbb Z^n$ then $\{e_1\otimes 1,...,e_n\otimes 1\}$ is a $\Bbb Q$-basis of $\Bbb Z^n\otimes \Bbb Q$

Published on 25 Mar 2020 - 10:20

score 53 · Answer 6 · 2026-03-25 16:02:32

53

Views

Checking that $\dfrac{\mathbb{Z}[x_1,x_2]}{\langle x_1^2\rangle}$ is a $\mathbb{Z}$-algebra

Published on 25 Mar 2026 - 16:02

score 70 · Answer 7 · 2026-03-26 12:38:34

70

Views

Are all faithful actions of finite rank free groups ping-pong actions?

Published on 26 Mar 2026 - 12:38

score 88 · Answer 8 · 2026-03-26 04:29:24

88

Views

Does there exist a two-generated simple non-abelian group with specific properties?

Published on 26 Mar 2026 - 4:29

score 145 · Answer 9 · 2020-04-01 04:12:34

145

Views

Show that the set of polynomials in $\mathbb{Q}[X]$ such that $f(\mathbb{Z}) \subset \mathbb{Z}$ is not Noetherian.

Published on 01 Apr 2020 - 4:12

score 169 · Answer 10 · 2020-04-01 18:25:17

169

Views

Finitely Generated Modules - Nakayama's Lemma proof

Published on 01 Apr 2020 - 18:25

score 394 · Answer 11 · 2026-03-26 14:29:29

394

Views

Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

Published on 26 Mar 2026 - 14:29

score 30 · Answer 12 · 2020-04-14 16:54:38

30

Views

"Minimal" type rank of finitely generated abelian groups with torsion

Published on 14 Apr 2020 - 16:54

score 72 · Answer 13 · 2020-04-14 23:16:53

72

Views

Proving or disproving that a nonidentity cyclic group has at least two generators.

Published on 14 Apr 2020 - 23:16

score 65 · Answer 14 · 2026-03-26 03:12:51

65

Views

This type of group of functions is never finitely generated. Proof?

Published on 26 Mar 2026 - 3:12

score 165 · Answer 15 · 2026-03-25 23:13:03

165

Views

Let $G=\langle x,y|x^{8}=y^{2}=e,yxyx^{3}=e \rangle$. Show that $|G|\leq16$. Assuming that $|G|=16$, find the center of $G$ and the order of xy.

Published on 25 Mar 2026 - 23:13

List Question

How should one interpret $R[A_1,..,A_n]$ where $R$ is a unital ring and $A_i\in M_{n\times n}(R)$

Number of maximal subgroups in finitely generated amenable groups

Can a quotient of a polynomial ring by $n-1$ polynomials make $n$ variables $m$th powers?

Torsion in finitely generated modules over polynomial rings

If $\{e_1,...,e_n\}$ is a $\Bbb Z$-basis of $\Bbb Z^n$ then $\{e_1\otimes 1,...,e_n\otimes 1\}$ is a $\Bbb Q$-basis of $\Bbb Z^n\otimes \Bbb Q$

Checking that $\dfrac{\mathbb{Z}[x_1,x_2]}{\langle x_1^2\rangle}$ is a $\mathbb{Z}$-algebra

Are all faithful actions of finite rank free groups ping-pong actions?

Does there exist a two-generated simple non-abelian group with specific properties?

Show that the set of polynomials in $\mathbb{Q}[X]$ such that $f(\mathbb{Z}) \subset \mathbb{Z}$ is not Noetherian.

Finitely Generated Modules - Nakayama's Lemma proof

Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

"Minimal" type rank of finitely generated abelian groups with torsion

Proving or disproving that a nonidentity cyclic group has at least two generators.

This type of group of functions is never finitely generated. Proof?

Let $G=\langle x,y|x^{8}=y^{2}=e,yxyx^{3}=e \rangle$. Show that $|G|\leq16$. Assuming that $|G|=16$, find the center of $G$ and the order of xy.

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