Question

Proving an Isomorphism between $\mathbb{R} / (f) $ and $\mathbb{R} / (x^2) $

score 63 · Answer 1 · 2020-03-04 18:16:31

63

Views

Proving an Isomorphism between $\mathbb{R} / (f) $ and $\mathbb{R} / (x^2) $

Published on 04 Mar 2020 - 18:16

score 185 · Answer 2 · 2020-03-05 01:06:36

185

Views

A question about prime ideal

Published on 05 Mar 2020 - 1:06

score 150 · Answer 3 · 2020-03-06 20:56:24

150

Views

Is $(\mathbb{Z}/5\mathbb{Z} \times \mathbb{Z}/3 \mathbb{Z})/\left<([0]_5,[2]_3)\right> \cong \mathbb{Z}/2\mathbb{Z} $?

Published on 06 Mar 2020 - 20:56

score 30 · Answer 4 · 2020-03-11 19:11:58

30

Views

Isomorphic field extenstion

Published on 11 Mar 2020 - 19:11

score 134 · Answer 5 · 2020-03-23 19:49:40

134

Views

Purely inseparable extensions vs subextensions

Published on 23 Mar 2020 - 19:49

score 1.3k · Answer 6 · 2020-03-30 15:19:32

1.3k

Views

Correspondence theorem in Ring theory

Published on 30 Mar 2020 - 15:19

score 315 · Answer 7 · 2026-03-25 21:49:57

315

Views

Isomorphism from $Z[i]/(p)$ to $(p^n)/(p^{n+1})$ where $p$ is a irreducible element .

Published on 25 Mar 2026 - 21:49

score 37 · Answer 8 · 2020-04-11 09:42:42

37

Views

Problem about kernels as ideals and the First Isomorphism Theorem

Published on 11 Apr 2020 - 9:42

score 82 · Answer 9 · 2020-04-18 13:46:41

82

Views

Let $\varphi\colon R\to(R/I)\oplus(R/J)$ where $\varphi(r) = (r + I, r + J)$. Show $\varphi$ is an isomorphism iff $I + J = R$ and $I \cap J = \{0\}$.

Published on 18 Apr 2020 - 13:46

score 108 · Answer 10 · 2020-04-26 16:50:00

108

Views

Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Published on 26 Apr 2020 - 16:50

score 126 · Answer 11 · 2026-03-25 19:05:05

126

Views

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

Published on 25 Mar 2026 - 19:05

score 49 · Answer 12 · 2020-05-02 07:41:45

49

Views

the isomorphism between two matrix groups

Published on 02 May 2020 - 7:41

score 598 · Answer 13 · 2020-05-03 15:27:57

598

Views

Proving the kernel of $\phi: \mathbb{Z}[x] \to \mathbb{Z}[i],\ p(x) \mapsto p(i)$ is the ideal generated by $(x^2+1)$

Published on 03 May 2020 - 15:27

score 42 · Answer 14 · 2020-05-07 03:59:52

42

Views

Number of ring automorhism of $\mathbb{Z}_4$?

Published on 07 May 2020 - 3:59

score 64 · Answer 15 · 2020-05-08 19:49:57

64

Views

Are the rings $\mathbb{Z}_2[X] /(X^2 + 1)$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$ isomorphic?

Published on 08 May 2020 - 19:49

List Question

Proving an Isomorphism between $\mathbb{R} / (f) $ and $\mathbb{R} / (x^2) $

A question about prime ideal

Is $(\mathbb{Z}/5\mathbb{Z} \times \mathbb{Z}/3 \mathbb{Z})/\left<([0]_5,[2]_3)\right> \cong \mathbb{Z}/2\mathbb{Z} $?

Isomorphic field extenstion

Purely inseparable extensions vs subextensions

Correspondence theorem in Ring theory

Isomorphism from $Z[i]/(p)$ to $(p^n)/(p^{n+1})$ where $p$ is a irreducible element .

Problem about kernels as ideals and the First Isomorphism Theorem

Let $\varphi\colon R\to(R/I)\oplus(R/J)$ where $\varphi(r) = (r + I, r + J)$. Show $\varphi$ is an isomorphism iff $I + J = R$ and $I \cap J = \{0\}$.

Are the ring $\mathbb{R}[x]/(x^{2})$ and $\mathbb{R}[x]/(x^{3})$ isomorphic?

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

the isomorphism between two matrix groups

Proving the kernel of $\phi: \mathbb{Z}[x] \to \mathbb{Z}[i],\ p(x) \mapsto p(i)$ is the ideal generated by $(x^2+1)$

Number of ring automorhism of $\mathbb{Z}_4$?

Are the rings $\mathbb{Z}_2[X] /(X^2 + 1)$ and $\mathbb{Z}_2 \times \mathbb{Z}_2$ isomorphic?

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