We know that if R is a noetherian ring then every submodule of a finitely generated module is finitely generated. In case R is absolutely flat, we have every finitely generated ideal is principal, can we extend this results to R- modules, i.e have we every finitely generated submodule of an R-module is cyclic?
2026-03-27 21:54:39.1774648479
When every finitely generated submodule of an R-module is cyclic?
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A module is called a Bézout module if its f.g. submodules are all cyclic. The resource I would recommend with the most contents about this type of module is