Item 50 (0516)—The Stacks project

Processing math: 100%

if $0 \to K \to L \to M \to 0$ is a short exact sequence of $R$ -modules and $K$ , $M$ are free, then $L$ is free,

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Comment #9999 by Informatika on February 21, 2025 at 06:49

Given that 𝐾 and 𝑀 are free 𝑅-modules in the short exact sequence 0→𝐾→𝐿→𝑀→ 0, is 𝐿 L necessarily free? Could the structure of 𝑅 influence this conclusion?

Regard Informatika

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