Question

Show that $\text{Frac}(\mathbb{Z}(\sqrt{2}))$ is isomorphic to $\mathbb{Q}(\sqrt{2})$

score 98 · Answer 1 · 2021-08-01 22:51:22

98

Views

Show that $\text{Frac}(\mathbb{Z}(\sqrt{2}))$ is isomorphic to $\mathbb{Q}(\sqrt{2})$

Published on 01 Aug 2021 - 22:51

score 131 · Answer 2 · 2021-08-07 22:16:50

131

Views

isomorphism $\psi$ between quotient rings

Published on 07 Aug 2021 - 22:16

score 359 · Answer 3 · 2026-02-23 13:06:25

359

Views

Proof of Dedekind-Kummer theorem

Published on 23 Feb 2026 - 13:06

score 141 · Answer 4 · 2021-08-26 12:55:59

141

Views

If $f :R \to S$ is an isomorphism from ring $R$ to ring $S$, both with identity, does $f(1_R) = 1_S$?

Published on 26 Aug 2021 - 12:55

score 54 · Answer 5 · 2021-09-26 04:14:33

54

Views

How to prove this isomorphism?

Published on 26 Sep 2021 - 4:14

score 528 · Answer 6 · 2021-10-25 14:18:05

528

Views

isomorphism $\mathbb{C} [X,Y]/(X^2 + Y^2 - 1)$

Published on 25 Oct 2021 - 14:18

score 90 · Answer 7 · 2021-10-30 08:58:54

90

Views

How to prove something is NOT a ring isomorphism?

Published on 30 Oct 2021 - 8:58

score 92 · Answer 8 · 2021-11-16 12:41:07

92

Views

Prove that for a finite field $R$ of characteristic $p$, the mapping $f(a)=a^p$ for every element $a$ of $R$ is an isomorphism.

Published on 16 Nov 2021 - 12:41

score 32 · Answer 9 · 2021-11-23 20:16:28

32

Views

Find all the ideals $\mathfrak{b}$ that fit $\mathfrak{a}\subsetneq\mathfrak{b}\subsetneq\mathbb{R}[X,Y,Z]$,being$\mathfrak{a}=(X^2-2X-4,Y-X^2,Z-X^3)$

Published on 23 Nov 2021 - 20:16

score 34 · Answer 10 · 2026-03-25 22:10:27

34

Views

Some Characterizations of Isoartinian Module

Published on 25 Mar 2026 - 22:10

score 36 · Answer 11 · 2021-12-14 12:59:16

36

Views

Prove: $F[t]/H[t]$ is isomorphic to $(F/H)[t]$

Published on 14 Dec 2021 - 12:59

score 46 · Answer 12 · 2021-12-14 14:09:07

46

Views

Given a proper field extension $L/K$, can we have $L\cong K$?

Published on 14 Dec 2021 - 14:09

score 20 · Answer 13 · 2026-03-25 23:35:22

20

Views

Doubts regarding correspondence theorem.

Published on 25 Mar 2026 - 23:35

score 51 · Answer 14 · 2026-03-26 01:07:27

51

Views

Over a left V-ring, why is every module containing a simple essential submodule is simple?

Published on 26 Mar 2026 - 1:07

score 179 · Answer 15 · 2021-12-29 17:36:33

179

Views

Showing that $\mathbb{Z}_{24}$ is not isomorphic to $\mathbb{Z}_{4}\times\mathbb{Z}_6$

Published on 29 Dec 2021 - 17:36

List Question

Show that $\text{Frac}(\mathbb{Z}(\sqrt{2}))$ is isomorphic to $\mathbb{Q}(\sqrt{2})$

isomorphism $\psi$ between quotient rings

Proof of Dedekind-Kummer theorem

If $f :R \to S$ is an isomorphism from ring $R$ to ring $S$, both with identity, does $f(1_R) = 1_S$?

How to prove this isomorphism?

isomorphism $\mathbb{C} [X,Y]/(X^2 + Y^2 - 1)$

How to prove something is NOT a ring isomorphism?

Prove that for a finite field $R$ of characteristic $p$, the mapping $f(a)=a^p$ for every element $a$ of $R$ is an isomorphism.

Find all the ideals $\mathfrak{b}$ that fit $\mathfrak{a}\subsetneq\mathfrak{b}\subsetneq\mathbb{R}[X,Y,Z]$,being$\mathfrak{a}=(X^2-2X-4,Y-X^2,Z-X^3)$

Some Characterizations of Isoartinian Module

Prove: $F[t]/H[t]$ is isomorphic to $(F/H)[t]$

Given a proper field extension $L/K$, can we have $L\cong K$?

Doubts regarding correspondence theorem.

Over a left V-ring, why is every module containing a simple essential submodule is simple?

Showing that $\mathbb{Z}_{24}$ is not isomorphic to $\mathbb{Z}_{4}\times\mathbb{Z}_6$

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