Let $R=\mathbb Z[X,Y]$. Find an exact sequence $0\to R\to R\oplus R \to R\xrightarrow{f} \mathbb Z \to 0$ with $f(g(x,y)) := g(0,0)$ for all $g \in R$

score 39 · Answer 9 · 2026-03-27 00:05:20

39

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Prove that an (additive) functor $F$ between abelian categories (categories of modules) that admits an exact left adjoint must preserve injectives

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score 43 · Answer 10 · 2024-02-29 20:35:26

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score 55 · Answer 11 · 2024-03-02 02:44:50

55

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score 59 · Answer 12 · 2024-03-11 11:09:30

59

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score 35 · Answer 13 · 2024-03-12 20:34:04

35

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score 11 · Answer 14 · 2026-02-26 05:54:05

11

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let R be local Noetherian. Any finitely generated R-module N st. any short exact sequence with $N$-ending is exact after tensor with R-module is free

Published on 26 Feb 2026 - 5:54

score 65 · Answer 15 · 2026-03-28 22:06:22

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A divisibility property in a sequence with exponential terms

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Let $R=\mathbb Z[X,Y]$. Find an exact sequence $0\to R\to R\oplus R \to R\xrightarrow{f} \mathbb Z \to 0$ with $f(g(x,y)) := g(0,0)$ for all $g \in R$

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