Question

Is $K:=\begin{pmatrix} 0 & \Bbb C \\ 0 & \Bbb C\end{pmatrix} \leq M_2(\Bbb C)$ simple in $M_2(\Bbb C)$?

score 62 · Answer 1 · 2026-04-15 17:17:03

62

Views

Is $K:=\begin{pmatrix} 0 & \Bbb C \\ 0 & \Bbb C\end{pmatrix} \leq M_2(\Bbb C)$ simple in $M_2(\Bbb C)$?

Published on 15 Apr 2026 - 17:17

score 53 · Answer 2 · 2026-04-15 23:15:11

53

Views

If $a^2=a\enspace\forall~a\in R$, then the ring $R$ is commutative

Published on 15 Apr 2026 - 23:15

score 143 · Answer 3 · 2026-04-14 18:39:48

143

Views

Necessity of the Cauchy product?

Published on 14 Apr 2026 - 18:39

score 32 · Answer 4 · 2026-04-15 03:04:47

32

Views

Rings in which $l_R(a) = Rb$ and $Ra = l_R(c)$ for each $a\in R$

Published on 15 Apr 2026 - 3:04

score 276 · Answer 5 · 2026-05-10 20:39:03

276

Views

Maximal ideals in the path algebra of a quiver

Published on 10 May 2026 - 20:39

score 175 · Answer 6 · 2026-04-08 06:32:44

175

Views

Prime Ideals in Rings of Fractions

Published on 08 Apr 2026 - 6:32

score 54 · Answer 7 · 2026-05-05 20:16:29

54

Views

Let $V_i\subset K$ be a family of valuation rings associated to field $K$. $D=\bigcap_iV_i$. Is $\mathrm{Frac}(D)=K$?

Published on 05 May 2026 - 20:16

score 161 · Answer 8 · 2026-04-16 05:40:47

161

Views

Prove that $R$ contains infinitely many maximal ideals

Published on 16 Apr 2026 - 5:40

score 39 · Answer 9 · 2026-04-17 06:07:59

39

Views

On the $R$-module $R:=\mathrm{M}_2(\Bbb C)$.

Published on 17 Apr 2026 - 6:07

score 148 · Answer 10 · 2026-05-05 20:16:17

148

Views

$(R,m)$ is a noetherian local ring. Suppose $\dim(R)=1$ and $m$ principal. Does it follow that $R$ is a domain?

Published on 05 May 2026 - 20:16

score 167 · Answer 11 · 2026-04-15 06:34:24

167

Views

Prove that for every ideal: $I_1I_2 \subset I_1 \cap I_2 \subset I_1 \subset I_1 +I_2$.

Published on 15 Apr 2026 - 6:34

score 89 · Answer 12 · 2026-04-11 13:13:31

89

Views

In a finite division Ring $a^{|D|} = a$.

Published on 11 Apr 2026 - 13:13

score 48 · Answer 13 · 2026-04-12 14:56:06

48

Views

Definition of a point annihilator

Published on 12 Apr 2026 - 14:56

score 114 · Answer 14 · 2026-04-15 20:27:20

114

Views

Irreducibility of $\sum_{n=0}^{101}\frac{x^n}{n!}$

Published on 15 Apr 2026 - 20:27

score 43 · Answer 15 · 2026-04-13 02:59:26

43

Views

Direct finiteness of linear operator ring in infinitely many dimensions

Published on 13 Apr 2026 - 2:59

List Question

Is $K:=\begin{pmatrix} 0 & \Bbb C \\ 0 & \Bbb C\end{pmatrix} \leq M_2(\Bbb C)$ simple in $M_2(\Bbb C)$?

If $a^2=a\enspace\forall~a\in R$, then the ring $R$ is commutative

Necessity of the Cauchy product?

Rings in which $l_R(a) = Rb$ and $Ra = l_R(c)$ for each $a\in R$

Maximal ideals in the path algebra of a quiver

Prime Ideals in Rings of Fractions

Let $V_i\subset K$ be a family of valuation rings associated to field $K$. $D=\bigcap_iV_i$. Is $\mathrm{Frac}(D)=K$?

Prove that $R$ contains infinitely many maximal ideals

On the $R$-module $R:=\mathrm{M}_2(\Bbb C)$.

$(R,m)$ is a noetherian local ring. Suppose $\dim(R)=1$ and $m$ principal. Does it follow that $R$ is a domain?

Prove that for every ideal: $I_1I_2 \subset I_1 \cap I_2 \subset I_1 \subset I_1 +I_2$.

In a finite division Ring $a^{|D|} = a$.

Definition of a point annihilator

Irreducibility of $\sum_{n=0}^{101}\frac{x^n}{n!}$

Direct finiteness of linear operator ring in infinitely many dimensions

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