Is the structure theorem on f.g. modules over a PID implied by the Remak-Krull-Schmidt theorem? Or are there f.g. modules over PIDs for which the latter theorem fails?
2026-03-27 10:32:59.1774607579
Does Remak-Krull-Schmidt implies structure theorem for fg modules over PID
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According to section $5.7$ of Popescu, Abelian Categories,
In the case of commutative semiartinian rings a module is finite iff is noetherian. In general, I think that that section is a very good reading.