Question

I'm confused by the last step when showing that $\Phi$ is well defined in the proof of 2nd isomorphism theorem for rings?

score 73 · Answer 1 · 2024-02-09 06:43:56

73

Views

I'm confused by the last step when showing that $\Phi$ is well defined in the proof of 2nd isomorphism theorem for rings?

Published on 09 Feb 2024 - 6:43

score 49 · Answer 2 · 2024-02-15 21:35:38

49

Views

over a Field extension

Published on 15 Feb 2024 - 21:35

score 63 · Answer 3 · 2024-02-25 23:08:16

63

Views

Prove that the rings $\mathbb{C}((z;\sigma))$ and $\mathbb{H}((x))$ are not isomorphic.

Published on 25 Feb 2024 - 23:08

score 76 · Answer 4 · 2026-03-26 01:10:45

76

Views

$\mathbb{R}$-Algebra isomorphism $\mathbb{C}[z;\sigma]\cong \mathbb{R} \langle x,y\rangle/(y^2+1,xy+yx)$

Published on 26 Mar 2026 - 1:10

score 43 · Answer 5 · 2024-02-27 14:34:27

43

Views

Formula for an inverse isomorphism of commutative rings.

Published on 27 Feb 2024 - 14:34

score 79 · Answer 6 · 2024-03-08 13:11:59

79

Views

Are $\mathbb{Z}_{(2)}$ and $\mathbb{Z}_{(3)}$ isomophic?

Published on 08 Mar 2024 - 13:11

score 130 · Answer 7 · 2024-03-21 10:23:33

130

Views

Automorphisms of group ring

Published on 21 Mar 2024 - 10:23

score 252 · Answer 8 · 2026-03-21 19:48:04

252

Views

Is $\operatorname{Mat}(2,\mathbb{R})$ isomorphic to $\operatorname{Mat}(3,\mathbb{R})$?

Published on 21 Mar 2026 - 19:48

score 191 · Answer 9 · 2026-02-23 06:24:24

191

Views

Homomorphic images of nth power of a division ring

Published on 23 Feb 2026 - 6:24

score 100 · Answer 10 · 2017-05-01 15:03:39

100

Views

Let $R = \{m+n\sqrt{2} \mid m,n\in\mathbb Z\}$ and let $I =\ldots$ Find the ring to which $R/I$ is isomorphic

Published on 01 May 2017 - 15:03

score 49 · Answer 11 · 2017-05-01 21:13:29

49

Views

In the ring $Dp=(a/b∈Q(D)|b∉P)$ where P is a prime ideal of D let m = (a/b∈dp a∈p) show m is an ideal of dp

Published on 01 May 2017 - 21:13

score 409 · Answer 12 · 2017-05-02 10:54:15

409

Views

Are the following pair of rings isomorphic? [Proof Verification]

Published on 02 May 2017 - 10:54

score 187 · Answer 13 · 2017-05-25 09:16:59

187

Views

Confused with injection and surjection on ring homomorphisms

Published on 25 May 2017 - 9:16

score 130 · Answer 14 · 2017-06-15 05:30:23

130

Views

Isomorphisim of quotient ring: $\mathbb{Z}[x, y]/(y+1) \cong \mathbb{Z}[x]$

Published on 15 Jun 2017 - 5:30

score 416 · Answer 15 · 2026-02-23 01:15:50

416

Views

Question about Boolean rings.

Published on 23 Feb 2026 - 1:15

List Question

I'm confused by the last step when showing that $\Phi$ is well defined in the proof of 2nd isomorphism theorem for rings?

over a Field extension

Prove that the rings $\mathbb{C}((z;\sigma))$ and $\mathbb{H}((x))$ are not isomorphic.

$\mathbb{R}$-Algebra isomorphism $\mathbb{C}[z;\sigma]\cong \mathbb{R} \langle x,y\rangle/(y^2+1,xy+yx)$

Formula for an inverse isomorphism of commutative rings.

Are $\mathbb{Z}_{(2)}$ and $\mathbb{Z}_{(3)}$ isomophic?

Automorphisms of group ring

Is $\operatorname{Mat}(2,\mathbb{R})$ isomorphic to $\operatorname{Mat}(3,\mathbb{R})$?

Homomorphic images of nth power of a division ring

Let $R = \{m+n\sqrt{2} \mid m,n\in\mathbb Z\}$ and let $I =\ldots$ Find the ring to which $R/I$ is isomorphic

In the ring $Dp=(a/b∈Q(D)|b∉P)$ where P is a prime ideal of D let m = (a/b∈dp a∈p) show m is an ideal of dp

Are the following pair of rings isomorphic? [Proof Verification]

Confused with injection and surjection on ring homomorphisms

Isomorphisim of quotient ring: $\mathbb{Z}[x, y]/(y+1) \cong \mathbb{Z}[x]$

Question about Boolean rings.

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