Question

Invariants of objects in $D(\mathcal{A})$ for non-hereditary category $\mathcal{A}$

score 64 · Answer 1 · 2026-03-27 16:27:43

64

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Invariants of objects in $D(\mathcal{A})$ for non-hereditary category $\mathcal{A}$

Published on 27 Mar 2026 - 16:27

score 81 · Answer 2 · 2022-11-29 03:29:08

81

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Let $g\in A$ be a regular element and $f\in A$, when do we have the preimage of $(x-f/g)\subset A_g[x]$ in $A[x]$ is $(gx-f)$?

Published on 29 Nov 2022 - 3:29

score 35 · Answer 3 · 2022-11-29 14:13:40

35

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Give an example of a ring $A$ and a multiplicative set $S$of $A$ such that $S^{-1}A$ is a PID (but not a field), but $A$ is not a PID.

Published on 29 Nov 2022 - 14:13

score 53 · Answer 4 · 2022-12-02 16:14:30

53

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Explicit Computation of Maps of Completed Local Rings of Curves

Published on 02 Dec 2022 - 16:14

score 78 · Answer 5 · 2022-12-04 13:27:07

78

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If $I$, $J$ are ideals, $S^{-1}(I \cap J)=S^{-1}I \cap S^{-1}J$

Published on 04 Dec 2022 - 13:27

score 41 · Answer 6 · 2022-12-05 14:46:56

41

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If $p|s$ for some $s \in S$ then $p/1 \in (S^{-1}R)^*$, where $p$ prime

Published on 05 Dec 2022 - 14:46

score 133 · Answer 7 · 2022-12-11 12:51:19

133

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A homomorphism $M \to N$ is surjective iff $M_\mathfrak{p} \to N_\mathfrak{p}$ is surjective for all $\mathfrak{p} \in \mathrm{Spec}(R)$ iff…

Published on 11 Dec 2022 - 12:51

score 96 · Answer 8 · 2022-12-19 14:16:40

96

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Questions of (9.3) from Atiyah's Introduction to Commutative Algebra

Published on 19 Dec 2022 - 14:16

score 132 · Answer 9 · 2022-12-21 04:40:57

132

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Intuition for localization of $\mathbb{Z}/6\mathbb{Z}$

Published on 21 Dec 2022 - 4:40

score 42 · Answer 10 · 2022-12-21 20:56:21

42

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If $S = \{(1, 1), (1, 0)\}$, then $R' \simeq S^{-1} (R' \times R'')$. (from Altman, Kleiman)

Published on 21 Dec 2022 - 20:56

score 54 · Answer 11 · 2022-12-22 20:15:00

54

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Are the two definitions of local objects in the context of left Bousfield localization equivalent?

Published on 22 Dec 2022 - 20:15

score 188 · Answer 12 · 2022-12-22 23:04:10

188

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Isomorphism of Tensor product of Localizations

Published on 22 Dec 2022 - 23:04

score 77 · Answer 13 · 2022-12-25 22:18:30

77

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When one defines the localized ring $A_f$, is it tacitly assumed that $f$ is not nilpotent?

Published on 25 Dec 2022 - 22:18

score 42 · Answer 14 · 2026-03-29 22:08:25

42

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Quotient of ideals of prime power in a localized integer ring

Published on 29 Mar 2026 - 22:08

score 56 · Answer 15 · 2023-01-02 16:53:26

56

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$\operatorname{Ann}_{R_\mathfrak{p}}(M_\mathfrak{p})=(\operatorname{Ann}_R(M))_\mathfrak{p}$

Published on 02 Jan 2023 - 16:53

List Question

Invariants of objects in $D(\mathcal{A})$ for non-hereditary category $\mathcal{A}$

Let $g\in A$ be a regular element and $f\in A$, when do we have the preimage of $(x-f/g)\subset A_g[x]$ in $A[x]$ is $(gx-f)$?

Give an example of a ring $A$ and a multiplicative set $S$of $A$ such that $S^{-1}A$ is a PID (but not a field), but $A$ is not a PID.

Explicit Computation of Maps of Completed Local Rings of Curves

If $I$, $J$ are ideals, $S^{-1}(I \cap J)=S^{-1}I \cap S^{-1}J$

If $p|s$ for some $s \in S$ then $p/1 \in (S^{-1}R)^*$, where $p$ prime

A homomorphism $M \to N$ is surjective iff $M_\mathfrak{p} \to N_\mathfrak{p}$ is surjective for all $\mathfrak{p} \in \mathrm{Spec}(R)$ iff…

Questions of (9.3) from Atiyah's Introduction to Commutative Algebra

Intuition for localization of $\mathbb{Z}/6\mathbb{Z}$

If $S = \{(1, 1), (1, 0)\}$, then $R' \simeq S^{-1} (R' \times R'')$. (from Altman, Kleiman)

Are the two definitions of local objects in the context of left Bousfield localization equivalent?

Isomorphism of Tensor product of Localizations

When one defines the localized ring $A_f$, is it tacitly assumed that $f$ is not nilpotent?

Quotient of ideals of prime power in a localized integer ring

$\operatorname{Ann}_{R_\mathfrak{p}}(M_\mathfrak{p})=(\operatorname{Ann}_R(M))_\mathfrak{p}$

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