Question

Algebra isomorphism between a localization of a ring $A$ and a quotient ring of $A[X]$

score 316 · Answer 1 · 2017-06-21 22:22:05

316

Views

Algebra isomorphism between a localization of a ring $A$ and a quotient ring of $A[X]$

Published on 21 Jun 2017 - 22:22

score 161 · Answer 2 · 2026-03-27 22:59:32

161

Views

"Small" valuation ring extensions

Published on 27 Mar 2026 - 22:59

score 922 · Answer 3 · 2026-03-30 04:24:52

922

Views

Is every $S^{-1}A$-module the localization of an $A$-module?

Published on 30 Mar 2026 - 4:24

score 1.5k · Answer 4 · 2026-03-27 03:45:03

1.5k

Views

Flat Modules and Localization at prime ideal

Published on 27 Mar 2026 - 3:45

score 77 · Answer 5 · 2017-06-28 01:10:33

77

Views

Why is $\operatorname{nilrad} R_S=\left(\operatorname{nilrad} R\right)_S$?

Published on 28 Jun 2017 - 1:10

score 78 · Answer 6 · 2017-07-01 17:14:22

78

Views

Let $i:M\to$ $N$ be an injection and let $f:M \to M/N$ is the canonical epimorphism, why $i_S$, $f_S$ are injective, surjective respectively?

Published on 01 Jul 2017 - 17:14

score 41 · Answer 7 · 2017-07-01 18:49:39

41

Views

Let $I'$ be a fractional ideal for $D_S$. Why $I'$ has the form $I_S$ for some fractional ideal $I$ in $D$?

Published on 01 Jul 2017 - 18:49

score 472 · Answer 8 · 2026-03-26 23:10:56

472

Views

Why the localization $D_P$ of a Dedekind domain $D$ at the prime ideal $P$ is a principal ideal domain?

Published on 26 Mar 2026 - 23:10

score 200 · Answer 9 · 2026-03-26 23:11:20

200

Views

If $D$ is Noetherian and $D_P$ is a discrete valuation ring, then $D$ is Dedekind?

Published on 26 Mar 2026 - 23:11

score 42 · Answer 10 · 2017-07-03 00:24:10

42

Views

Why $F$ is the field of fractions of $D_S$?

Published on 03 Jul 2017 - 0:24

score 160 · Answer 11 · 2017-07-03 14:43:54

160

Views

Is every $S^{-1}A$-module homomorphism $f:N \to N'$ induced by an $A$-module homomorphism?

Published on 03 Jul 2017 - 14:43

score 1.2k · Answer 12 · 2017-07-07 21:28:29

1.2k

Views

Complete Ring of Fractions of $\mathbb{Z}_{n}$ for any $n$

Published on 07 Jul 2017 - 21:28

score 220 · Answer 13 · 2017-07-08 21:43:08

220

Views

Rings of fractions for all possible sets of denominators

Published on 08 Jul 2017 - 21:43

score 423 · Answer 14 · 2026-03-26 17:36:19

423

Views

Showing isomorphism between two rings of fractions

Published on 26 Mar 2026 - 17:36

score 434 · Answer 15 · 2026-03-28 15:26:18

434

Views

Basis of the localization of module

Published on 28 Mar 2026 - 15:26

List Question

Algebra isomorphism between a localization of a ring $A$ and a quotient ring of $A[X]$

"Small" valuation ring extensions

Is every $S^{-1}A$-module the localization of an $A$-module?

Flat Modules and Localization at prime ideal

Why is $\operatorname{nilrad} R_S=\left(\operatorname{nilrad} R\right)_S$?

Let $i:M\to$ $N$ be an injection and let $f:M \to M/N$ is the canonical epimorphism, why $i_S$, $f_S$ are injective, surjective respectively?

Let $I'$ be a fractional ideal for $D_S$. Why $I'$ has the form $I_S$ for some fractional ideal $I$ in $D$?

Why the localization $D_P$ of a Dedekind domain $D$ at the prime ideal $P$ is a principal ideal domain?

If $D$ is Noetherian and $D_P$ is a discrete valuation ring, then $D$ is Dedekind?

Why $F$ is the field of fractions of $D_S$?

Is every $S^{-1}A$-module homomorphism $f:N \to N'$ induced by an $A$-module homomorphism?

Complete Ring of Fractions of $\mathbb{Z}_{n}$ for any $n$

Rings of fractions for all possible sets of denominators

Showing isomorphism between two rings of fractions

Basis of the localization of module

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