Question

$F,G\in k[x,y]$ are coprime $\Rightarrow $ every element in $\mathscr{O}_P/\langle F,G\rangle$ has a polynomial representative

score 298 · Answer 1 · 2020-10-01 19:51:26

298

Views

$F,G\in k[x,y]$ are coprime $\Rightarrow $ every element in $\mathscr{O}_P/\langle F,G\rangle$ has a polynomial representative

Published on 01 Oct 2020 - 19:51

score 119 · Answer 2 · 2020-10-15 18:27:21

119

Views

Classification of local subrings of fields of rational functions on projective curves

Published on 15 Oct 2020 - 18:27

score 117 · Answer 3 · 2020-10-16 05:27:21

117

Views

Finite Local Homomorphisms and Primary Ideals

Published on 16 Oct 2020 - 5:27

score 234 · Answer 4 · 2020-10-27 07:42:50

234

Views

Is the completion ring map $A\to \hat{A}$ formally unramified/ramified/weakly etale/etale?

Published on 27 Oct 2020 - 7:42

score 249 · Answer 5 · 2026-03-27 04:57:09

249

Views

A plane curve of degree 3 with three singular points

Published on 27 Mar 2026 - 4:57

score 113 · Answer 6 · 2020-10-28 17:44:36

113

Views

Trying to delete in a sum of ideals: P+I=Q+I so P=Q?

Published on 28 Oct 2020 - 17:44

score 74 · Answer 7 · 2020-10-31 11:01:30

74

Views

Does the existence of solutions of $P(x)\equiv 0\pmod{\mathfrak{m}^n}$ for all $n$ gives a solution of $P(x)=0$?

Published on 31 Oct 2020 - 11:01

score 86 · Answer 8 · 2020-11-01 08:33:08

86

Views

Let $M$ be the only maximal ideal of the local ring $\Bbb{Z}_{(p)}$, show that $\Bbb{Z}_{(p)}/M$ is isomorphic to $\Bbb{Z}/(p)$.

Published on 01 Nov 2020 - 8:33

score 47 · Answer 9 · 2020-11-18 14:31:52

47

Views

Understanding the definition of a local ring.

Published on 18 Nov 2020 - 14:31

score 216 · Answer 10 · 2020-11-19 01:02:55

216

Views

Show that $R^* = R\setminus \mathfrak{m}.$

Published on 19 Nov 2020 - 1:02

score 502 · Answer 11 · 2020-11-19 12:22:48

502

Views

My trial for showing that $K[[x]]$ over a field is a local ring.

Published on 19 Nov 2020 - 12:22

score 271 · Answer 12 · 2020-11-23 19:12:19

271

Views

Complete Noetherian local ring with residue field $\mathbb{F}_p$ is an algebra over the $p$-adic integers $\mathbb{Z}_p$

Published on 23 Nov 2020 - 19:12

score 1k · Answer 13 · 2020-11-25 19:43:03

1k

Views

Local ring of a generic point on an integral scheme is a field

Published on 25 Nov 2020 - 19:43

score 299 · Answer 14 · 2020-12-07 09:42:33

299

Views

Every element of a local ring is a sum of two units iff the cardinality of the ring is less than twice the cardinality of units

Published on 07 Dec 2020 - 9:42

score 95 · Answer 15 · 2026-02-23 06:18:37

95

Views

Ring structure on a space of functions between vector spaces?

Published on 23 Feb 2026 - 6:18

List Question

$F,G\in k[x,y]$ are coprime $\Rightarrow $ every element in $\mathscr{O}_P/\langle F,G\rangle$ has a polynomial representative

Classification of local subrings of fields of rational functions on projective curves

Finite Local Homomorphisms and Primary Ideals

Is the completion ring map $A\to \hat{A}$ formally unramified/ramified/weakly etale/etale?

A plane curve of degree 3 with three singular points

Trying to delete in a sum of ideals: P+I=Q+I so P=Q?

Does the existence of solutions of $P(x)\equiv 0\pmod{\mathfrak{m}^n}$ for all $n$ gives a solution of $P(x)=0$?

Let $M$ be the only maximal ideal of the local ring $\Bbb{Z}_{(p)}$, show that $\Bbb{Z}_{(p)}/M$ is isomorphic to $\Bbb{Z}/(p)$.

Understanding the definition of a local ring.

Show that $R^* = R\setminus \mathfrak{m}.$

My trial for showing that $K[[x]]$ over a field is a local ring.

Complete Noetherian local ring with residue field $\mathbb{F}_p$ is an algebra over the $p$-adic integers $\mathbb{Z}_p$

Local ring of a generic point on an integral scheme is a field

Every element of a local ring is a sum of two units iff the cardinality of the ring is less than twice the cardinality of units

Ring structure on a space of functions between vector spaces?

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