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indécomposable - translation to french
Indecomposable representation
indécomposable
indecomposable
Definition
Indecomposable
·adj Not decomposable; incapable or difficult of decomposition; not resolvable into its constituents or elements.
Wikipedia
Indecomposable module
In abstract algebra, a module is indecomposable if it is non-zero and cannot be written as a direct sum of two non-zero submodules.
Indecomposable is a weaker notion than simple module (which is also sometimes called irreducible module): simple means "no proper submodule" , while indecomposable "not expressible as ".
A direct sum of indecomposables is called completely decomposable; this is weaker than being semisimple, which is a direct sum of simple modules.
A direct sum decomposition of a module into indecomposable modules is called an indecomposable decomposition.
