Question

$K[X]_X$ is not integral over $K[X]$

score 496 · Answer 1 · 2026-02-23 04:19:04

496

Views

$K[X]_X$ is not integral over $K[X]$

Published on 23 Feb 2026 - 4:19

score 989 · Answer 2 · 2019-03-06 19:03:05

989

Views

Show that every non-zero ideal of the ring of rationals with odd denominator is generated by $2^{n}$

Published on 06 Mar 2019 - 19:03

score 143 · Answer 3 · 2019-03-06 23:52:28

143

Views

Equivalent conditions involving (co)primary module (Proposition 3.9 from Eisenbud)

Published on 06 Mar 2019 - 23:52

score 150 · Answer 4 · 2019-03-07 00:20:39

150

Views

An equivalent condition for the localization map $M\to M_P$ to be injective

Published on 07 Mar 2019 - 0:20

score 166 · Answer 5 · 2019-03-07 02:11:50

166

Views

On modules in which tensor of each two elements is commutative

Published on 07 Mar 2019 - 2:11

score 93 · Answer 6 · 2026-03-25 12:28:08

93

Views

$R_{\mathfrak{p}}$ is integrally closed in its total quotient ring, then $R$ is integrally closed in its total quotient ring.

Published on 25 Mar 2026 - 12:28

score 39 · Answer 7 · 2019-03-10 01:07:54

39

Views

The map $M[f^{-1}]\to M[f^{-1}g^{-1}]$

Published on 10 Mar 2019 - 1:07

score 189 · Answer 8 · 2026-03-25 09:28:52

189

Views

The localization of the ring $\mathbb{Z} \times \mathbb{Z}$ at every prime ideal is an integral domain

Published on 25 Mar 2026 - 9:28

score 248 · Answer 9 · 2026-03-26 01:25:12

248

Views

if $M \otimes_A (A_m/mA_m)=0$ for every maximal ideal $m \subset A$, then $M=0$, $M$ finitely generated

Published on 26 Mar 2026 - 1:25

score 233 · Answer 10 · 2019-03-12 23:43:51

233

Views

Intersection of the kernels of localization maps

Published on 12 Mar 2019 - 23:43

score 61 · Answer 11 · 2019-03-17 18:42:23

61

Views

Commutative ring with finitely many minimal primes

Published on 17 Mar 2019 - 18:42

score 317 · Answer 12 · 2019-03-18 03:39:00

317

Views

Localization of $k[t]$ at a prime ideal is not a finitely generated $k[t]$-algebra?

Published on 18 Mar 2019 - 3:39

score 62 · Answer 13 · 2026-03-25 13:57:08

62

Views

If $\mathfrak{p}$ is a prime such that $M_\mathfrak{p} \neq 0$, then $\mathfrak{p}$ contains an associated prime of $M$

Published on 25 Mar 2026 - 13:57

score 68 · Answer 14 · 2026-03-25 03:07:31

68

Views

Show that $\equiv$ is a congruence on $M\times S$

Published on 25 Mar 2026 - 3:07

score 63 · Answer 15 · 2019-03-24 16:35:21

63

Views

When is this statement true $\frac{a}{s} \in S^{-1}I \implies a \in I$?

Published on 24 Mar 2019 - 16:35

List Question

$K[X]_X$ is not integral over $K[X]$

Show that every non-zero ideal of the ring of rationals with odd denominator is generated by $2^{n}$

Equivalent conditions involving (co)primary module (Proposition 3.9 from Eisenbud)

An equivalent condition for the localization map $M\to M_P$ to be injective

On modules in which tensor of each two elements is commutative

$R_{\mathfrak{p}}$ is integrally closed in its total quotient ring, then $R$ is integrally closed in its total quotient ring.

The map $M[f^{-1}]\to M[f^{-1}g^{-1}]$

The localization of the ring $\mathbb{Z} \times \mathbb{Z}$ at every prime ideal is an integral domain

if $M \otimes_A (A_m/mA_m)=0$ for every maximal ideal $m \subset A$, then $M=0$, $M$ finitely generated

Intersection of the kernels of localization maps

Commutative ring with finitely many minimal primes

Localization of $k[t]$ at a prime ideal is not a finitely generated $k[t]$-algebra?

If $\mathfrak{p}$ is a prime such that $M_\mathfrak{p} \neq 0$, then $\mathfrak{p}$ contains an associated prime of $M$

Show that $\equiv$ is a congruence on $M\times S$

When is this statement true $\frac{a}{s} \in S^{-1}I \implies a \in I$?

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