Question

Show that the solutions lifted by Hensel's lemma, are the only solutions in $\mathbb{Z} / p^k \mathbb{Z}$

score 299 · Answer 1 · 2026-04-14 15:53:10

299

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Show that the solutions lifted by Hensel's lemma, are the only solutions in $\mathbb{Z} / p^k \mathbb{Z}$

Published on 14 Apr 2026 - 15:53

score 2k · Answer 2 · 2026-04-16 23:07:04

2k

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Are $R=K[a,b,c,d]/(ad-bc, a^2c-b^3, bd^2-c^3, ac^2-b^2d)$ and $K[x^4,x^3y,xy^3,y^4]$ isomorphic?

Published on 16 Apr 2026 - 23:07

score 46 · Answer 3 · 2026-04-14 22:22:24

46

Views

Show by explicit calculation that $\varphi\colon\mathbb{Z}\to\mathbb{Z}_n, m\mapsto m\% n$ is a surjective ringhomomophism

Published on 14 Apr 2026 - 22:22

score 737 · Answer 4 · 2026-04-12 00:48:57

737

Views

What's the point of defining left ideals?

Published on 12 Apr 2026 - 0:48

score 47 · Answer 5 · 2026-04-09 00:05:25

47

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Notation Question about Rings

Published on 09 Apr 2026 - 0:05

score 362 · Answer 6 · 2026-04-13 13:39:59

362

Views

Ring of fractions $S^{-1}A$ and localisation

Published on 13 Apr 2026 - 13:39

score 560 · Answer 7 · 2026-04-14 14:09:04

560

Views

Show: $\varphi\colon\mathbb{Z}_{mn}\to\mathbb{Z}_m\times\mathbb{Z}_n, k\mapsto (k\% m,k\% n)$ is a ring isomorphism for $m$ and $n$ relatively prim

Published on 14 Apr 2026 - 14:09

score 662 · Answer 8 · 2026-04-13 14:01:52

662

Views

Sub-modules of free modules

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score 70 · Answer 9 · 2026-04-13 16:06:50

70

Views

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score 237 · Answer 10 · 2026-04-11 16:13:38

237

Views

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Published on 11 Apr 2026 - 16:13

score 601 · Answer 11 · 2026-04-12 04:47:24

601

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score 372 · Answer 12 · 2026-04-17 12:34:47

372

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Published on 17 Apr 2026 - 12:34

score 687 · Answer 13 · 2026-04-14 14:24:54

687

Views

Sylvester domains

Published on 14 Apr 2026 - 14:24

score 58 · Answer 14 · 2026-04-11 11:45:31

58

Views

How to show $c-b\lt b-a$

Published on 11 Apr 2026 - 11:45

score 68 · Answer 15 · 2026-04-15 09:48:39

68

Views

$V(\mathfrak{a} \cap \mathfrak{b}) = V(\mathfrak{a}) \cup V(\mathfrak{b})$ (Spectrum of a commutative ring)

Published on 15 Apr 2026 - 9:48

List Question

Show that the solutions lifted by Hensel's lemma, are the only solutions in $\mathbb{Z} / p^k \mathbb{Z}$

Are $R=K[a,b,c,d]/(ad-bc, a^2c-b^3, bd^2-c^3, ac^2-b^2d)$ and $K[x^4,x^3y,xy^3,y^4]$ isomorphic?

Show by explicit calculation that $\varphi\colon\mathbb{Z}\to\mathbb{Z}_n, m\mapsto m\% n$ is a surjective ringhomomophism

What's the point of defining left ideals?

Notation Question about Rings

Ring of fractions $S^{-1}A$ and localisation

Show: $\varphi\colon\mathbb{Z}_{mn}\to\mathbb{Z}_m\times\mathbb{Z}_n, k\mapsto (k\% m,k\% n)$ is a ring isomorphism for $m$ and $n$ relatively prim

Sub-modules of free modules

Proving that $V(R^*)=V(R)-1$

$\Bbb Z[i\alpha]$ UFD's

Questions on a proof of "All prime ideals of a Dedekind domain are invertible"

Global dimension of $\mathbb Q [x]$

Sylvester domains

How to show $c-b\lt b-a$

$V(\mathfrak{a} \cap \mathfrak{b}) = V(\mathfrak{a}) \cup V(\mathfrak{b})$ (Spectrum of a commutative ring)

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