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Results tagged with short-exact-sequences
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user 2083
For questions about short exact sequences in various contexts, including questions on short exact sequences of groups or modules.
54
votes
Accepted
Do all exact $1 \to A \to A \times B \to B \to 1$ split for finite groups?
This is true (1). It was extended to finitely generated profinite groups here (2). Surprisingly, it is also true in the category of finitely generated modules over a Noetherian commutative ring (3).
…
- 12.9k
26
votes
Short exact sequences every mathematician should know
Given a finitely generated module $M$ over a commutative Noetherian ring $R$, there is a short exact sequence $$0\to M_1 \to R^n \to M\to 0$$
where you map $1$ in each $R$ to a generator of $M$ and $M …
- 30.6k