Question

$\gamma$ is an inveterible matrix such that $a=b \gamma$, then why is it that we have $\oplus_{i=1}^n Ra_i \subseteq \oplus_{i=1}^n Rb_i$

score 36 · Answer 1 · 2026-04-15 02:45:19

36

Views

$\gamma$ is an inveterible matrix such that $a=b \gamma$, then why is it that we have $\oplus_{i=1}^n Ra_i \subseteq \oplus_{i=1}^n Rb_i$

Published on 15 Apr 2026 - 2:45

score 131 · Answer 2 · 2026-04-16 06:33:48

131

Views

Ring $C([0,1])$

Published on 16 Apr 2026 - 6:33

score 258 · Answer 3 · 2026-04-17 13:01:31

258

Views

Let $M$ be a semisimple right module over the ring $R$, and let $T:= End_{R}(M)$, $M$ is a semisimple left module over the ring $T$.

Published on 17 Apr 2026 - 13:01

score 67 · Answer 4 · 2026-04-15 22:00:37

67

Views

Aluffi, Exercise III.3.11: Only ring homomorphism from $R$ to $\mathbb{R}$ if $\mathbb{C}$ is a subring is the trivial homomorphism.

Published on 15 Apr 2026 - 22:00

score 50 · Answer 5 · 2026-04-17 06:29:13

50

Views

Showing $\mathbb{k}[x, y] / \langle y-x^2 \rangle \simeq \mathbb{k}[\bar x] $

Published on 17 Apr 2026 - 6:29

score 91 · Answer 6 · 2026-04-15 19:21:34

91

Views

Why the annihilator $\text{Ann}^{M}(a)$, with respect modules, not one sided?

Published on 15 Apr 2026 - 19:21

score 736 · Answer 7 · 2026-04-25 20:02:31

736

Views

Prove that $F(\alpha) = F(\alpha^{-1})$ if $\alpha \in \mathbb{C}$ is algebraic over $F$

Published on 25 Apr 2026 - 20:02

score 254 · Answer 8 · 2026-04-11 20:38:57

254

Views

Is there any example of a simple Abelian ring which is not domain?

Published on 11 Apr 2026 - 20:38

score 57 · Answer 9 · 2026-04-11 10:47:00

57

Views

Step of a proof in $R$-modules

Published on 11 Apr 2026 - 10:47

score 157 · Answer 10 · 2026-04-10 19:36:22

157

Views

Confusion on Monomial ideals

Published on 10 Apr 2026 - 19:36

score 189 · Answer 11 · 2026-03-26 11:04:50

189

Views

Polynomial rings and quotients of homogeneous ideals

Published on 26 Mar 2026 - 11:04

score 204 · Answer 12 · 2026-03-25 23:53:01

204

Views

In a non-commutative ring (possibly without identity) with no nontrivial automorphisms, do nilpotent elements form an ideal?

Published on 25 Mar 2026 - 23:53

score 103 · Answer 13 · 2026-04-09 12:55:14

103

Views

About radical of ideal

Published on 09 Apr 2026 - 12:55

score 94 · Answer 14 · 2026-05-06 10:42:10

94

Views

In $\mathbb{C}[a_{11}, \ldots, a_{nn}, b_{11}, \ldots, b_{nn}]$, is $\langle AB - I_n \rangle = \langle BA - I_n \rangle$?

Published on 06 May 2026 - 10:42

score 942 · Answer 15 · 2026-04-09 00:14:38

942

Views

Property of ideals

Published on 09 Apr 2026 - 0:14

List Question

$\gamma$ is an inveterible matrix such that $a=b \gamma$, then why is it that we have $\oplus_{i=1}^n Ra_i \subseteq \oplus_{i=1}^n Rb_i$

Ring $C([0,1])$

Let $M$ be a semisimple right module over the ring $R$, and let $T:= End_{R}(M)$, $M$ is a semisimple left module over the ring $T$.

Aluffi, Exercise III.3.11: Only ring homomorphism from $R$ to $\mathbb{R}$ if $\mathbb{C}$ is a subring is the trivial homomorphism.

Showing $\mathbb{k}[x, y] / \langle y-x^2 \rangle \simeq \mathbb{k}[\bar x] $

Why the annihilator $\text{Ann}^{M}(a)$, with respect modules, not one sided?

Prove that $F(\alpha) = F(\alpha^{-1})$ if $\alpha \in \mathbb{C}$ is algebraic over $F$

Is there any example of a simple Abelian ring which is not domain?

Step of a proof in $R$-modules

Confusion on Monomial ideals

Polynomial rings and quotients of homogeneous ideals

In a non-commutative ring (possibly without identity) with no nontrivial automorphisms, do nilpotent elements form an ideal?

About radical of ideal

In $\mathbb{C}[a_{11}, \ldots, a_{nn}, b_{11}, \ldots, b_{nn}]$, is $\langle AB - I_n \rangle = \langle BA - I_n \rangle$?

Property of ideals

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