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What (who) is indécomposable - definition
Indecomposable representation
Indecomposable distribution
PROBABILITY DISTRIBUTION
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In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables: Z ≠ X + Y. If it can be so expressed, it is decomposable: Z = X + Y.
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. Jacobson (2009), p.
Principal indecomposable module
SPECIAL KIND OF MODULE IN REPRESENTATION THEORY
Projective indecomposable module
In mathematics, especially in the area of abstract algebra known as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective modules, and indecomposable modules.
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.
