Question

Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$

score 81 · Answer 1 · 2019-02-26 12:44:51

Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$

Published on 26 Feb 2019 - 12:44

score 84 · Answer 2 · 2019-02-26 12:49:00

Finding a subring of $M(2,\mathbb{Q})$ which is isomorphic to a) $\mathbb{Q}\times \mathbb{Q}$ b)$\mathbb{Q}$ c)$\frac{\mathbb{Q}[x]}{(x^2)}$.

score 45 · Answer 3 · 2019-02-26 16:59:19

45

Views

Is $\mathbb{R}[x^3]$ $ \subseteq$ $\mathbb{R}[x]$?

Published on 26 Feb 2019 - 16:59

score 83 · Answer 4 · 2026-03-29 14:21:49

83

Views

Prove $\mathbb{Z}[\omega]/\left\langle p\right \rangle \cong \mathbb{F}_p[x]/\left \langle x^2+x+1 \right \rangle$

Published on 29 Mar 2026 - 14:21

score 3.4k · Answer 5 · 2026-03-30 13:21:31

3.4k

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How to find an ideal of a ring

Published on 30 Mar 2026 - 13:21

score 68 · Answer 6 · 2026-03-31 10:13:42

68

Views

If $(x-a)^2|f(x)$, then $(x-a)|f'(x)$ and if $(x-a)|f(x)$ and $(x-a)|f'(x)$, then $(x-a)^2|f(x)$

Published on 31 Mar 2026 - 10:13

score 120 · Answer 7 · 2019-02-27 01:18:05

120

Views

If $R$ is a simple ring and $n \in \Bbb Z$, show that either $nR = 0$ or $nr=0$ implies that $r=0$

Published on 27 Feb 2019 - 1:18

score 366 · Answer 8 · 2019-02-27 03:11:56

366

Views

Let $R$ be a commutative ring. Take $a,b \in R$, if $Ra + Rb = R$, show that $Ra \cap Rb \subset Rab$.

Published on 27 Feb 2019 - 3:11

score 48 · Answer 9 · 2026-03-30 18:06:06

48

Views

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

Published on 30 Mar 2026 - 18:06

score 778 · Answer 10 · 2026-03-26 18:50:47

778

Views

Factor $X^4 + 3$ into irreducible factors in $F_7[X]$

Published on 26 Mar 2026 - 18:50

score 157 · Answer 11 · 2026-03-27 16:47:03

157

Views

An example of commutative ring which has conditions regarding Jacobson radical

Published on 27 Mar 2026 - 16:47

score 73 · Answer 12 · 2026-03-25 09:34:45

73

Views

Understanding old question proof about Dedekind domain

Published on 25 Mar 2026 - 9:34

score 224 · Answer 13 · 2026-03-25 06:13:09

224

Views

What is the significance of the precedence of a semiring/ ring operations?

Published on 25 Mar 2026 - 6:13

score 441 · Answer 14 · 2026-03-25 17:39:30

441

Views

Proving that "Giving a DVR with quotient field K is equivalent to defining an order function on K"

Published on 25 Mar 2026 - 17:39

score 263 · Answer 15 · 2026-03-25 07:42:45

263

Views

Finding an isomorphic subring of matrices

Published on 25 Mar 2026 - 7:42

List Question

Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$

Finding a subring of $M(2,\mathbb{Q})$ which is isomorphic to a) $\mathbb{Q}\times \mathbb{Q}$ b)$\mathbb{Q}$ c)$\frac{\mathbb{Q}[x]}{(x^2)}$.

Is $\mathbb{R}[x^3]$ $ \subseteq$ $\mathbb{R}[x]$?

Prove $\mathbb{Z}[\omega]/\left\langle p\right \rangle \cong \mathbb{F}_p[x]/\left \langle x^2+x+1 \right \rangle$

How to find an ideal of a ring

If $(x-a)^2|f(x)$, then $(x-a)|f'(x)$ and if $(x-a)|f(x)$ and $(x-a)|f'(x)$, then $(x-a)^2|f(x)$

If $R$ is a simple ring and $n \in \Bbb Z$, show that either $nR = 0$ or $nr=0$ implies that $r=0$

Let $R$ be a commutative ring. Take $a,b \in R$, if $Ra + Rb = R$, show that $Ra \cap Rb \subset Rab$.

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

Factor $X^4 + 3$ into irreducible factors in $F_7[X]$

An example of commutative ring which has conditions regarding Jacobson radical

Understanding old question proof about Dedekind domain

What is the significance of the precedence of a semiring/ ring operations?

Proving that "Giving a DVR with quotient field K is equivalent to defining an order function on K"

Finding an isomorphic subring of matrices

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