Question

When the localization of a ring is a finitely generated module over the ring via the canonical map from the ring to the localization

score 525 · Answer 1 · 2026-03-29 12:05:13

525

Views

When the localization of a ring is a finitely generated module over the ring via the canonical map from the ring to the localization

Published on 29 Mar 2026 - 12:05

score 928 · Answer 2 · 2017-08-29 15:59:31

928

Views

commutative rings whose localization at every prime ideal is a field

Published on 29 Aug 2017 - 15:59

score 690 · Answer 3 · 2026-03-26 22:58:38

690

Views

The Ring of Regular Functions for an Algebraic Set

Published on 26 Mar 2026 - 22:58

score 141 · Answer 4 · 2017-09-04 11:36:39

141

Views

$a,b$ co-prime elements in PID $R$ , then to show $R[X]/(aX-b) \cong R[1/a]$

Published on 04 Sep 2017 - 11:36

score 2k · Answer 5 · 2017-09-04 15:24:51

2k

Views

$\mathfrak p$ be a prime ideal of a commutative ring $R$ , then $R_\mathfrak p/\mathfrak pR_\mathfrak p$ is the field of fractions of $R/\mathfrak p$?

Published on 04 Sep 2017 - 15:24

score 54 · Answer 6 · 2026-03-27 03:43:01

54

Views

$R$ be a commutative ring , $A$ be an $R$-algebra , $M$ be an $A$-module , $M_m$ is flat over $R_{m\cap R}$ for every $m\in max(A)$

Published on 27 Mar 2026 - 3:43

score 105 · Answer 7 · 2017-09-08 14:16:47

105

Views

Localization as a quotient

Published on 08 Sep 2017 - 14:16

score 812 · Answer 8 · 2026-03-26 17:36:03

812

Views

Isomorphism in localization of rings

Published on 26 Mar 2026 - 17:36

score 213 · Answer 9 · 2017-09-11 22:30:43

213

Views

Localization and common zero set (basic algebraic geometry)

Published on 11 Sep 2017 - 22:30

score 43 · Answer 10 · 2017-09-17 12:53:17

43

Views

What is the meaning of $\mathbb C[t]_t$ in the theory of local ring?

Published on 17 Sep 2017 - 12:53

score 97 · Answer 11 · 2026-03-27 03:41:54

97

Views

How can I show flatness of this morphism using local algebra?

Published on 27 Mar 2026 - 3:41

score 162 · Answer 12 · 2017-09-19 02:59:12

162

Views

If $R$ is a ring and $M$ be any maximal ideal with $a\notin M$, then there exists $q\in M$ and $s\in R$ such that forall $r\in R$ $r=sar+qr$

Published on 19 Sep 2017 - 2:59

score 260 · Answer 13 · 2017-09-19 17:30:19

260

Views

Localization Isomorphisms (hint)

Published on 19 Sep 2017 - 17:30

score 328 · Answer 14 · 2017-09-20 00:33:36

328

Views

Bijection between prime ideals of $\Bbb C[x,y]$ which contains the ideal $(xy-1)$ and the prime ideals in $\Bbb C[x]$ which does not contain $x$

Published on 20 Sep 2017 - 0:33

score 51 · Answer 15 · 2026-03-29 12:11:54

51

Views

Is it always possible to recover an affine morphism by restricting a finite-type morphism?

Published on 29 Mar 2026 - 12:11

List Question

When the localization of a ring is a finitely generated module over the ring via the canonical map from the ring to the localization

commutative rings whose localization at every prime ideal is a field

The Ring of Regular Functions for an Algebraic Set

$a,b$ co-prime elements in PID $R$ , then to show $R[X]/(aX-b) \cong R[1/a]$

$\mathfrak p$ be a prime ideal of a commutative ring $R$ , then $R_\mathfrak p/\mathfrak pR_\mathfrak p$ is the field of fractions of $R/\mathfrak p$?

$R$ be a commutative ring , $A$ be an $R$-algebra , $M$ be an $A$-module , $M_m$ is flat over $R_{m\cap R}$ for every $m\in max(A)$

Localization as a quotient

Isomorphism in localization of rings

Localization and common zero set (basic algebraic geometry)

What is the meaning of $\mathbb C[t]_t$ in the theory of local ring?

How can I show flatness of this morphism using local algebra?

If $R$ is a ring and $M$ be any maximal ideal with $a\notin M$, then there exists $q\in M$ and $s\in R$ such that forall $r\in R$ $r=sar+qr$

Localization Isomorphisms (hint)

Bijection between prime ideals of $\Bbb C[x,y]$ which contains the ideal $(xy-1)$ and the prime ideals in $\Bbb C[x]$ which does not contain $x$

Is it always possible to recover an affine morphism by restricting a finite-type morphism?

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