Module theory

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. (Wikipedia).

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From playlist Solve a System of Inequalities by Graphing

Related pages

Prime ideal | Vector space | Krull–Schmidt theorem | Direct sum of modules | Semisimple module | Prüfer group | Fitting lemma | Rational number | Principal ideal domain | Irreducibility (mathematics) | Field (mathematics) | Integer | Idempotent (ring theory) | Simple module | Real number | Endomorphism ring | Structure theorem for finitely generated modules over a principal ideal domain | Prime number | Abstract algebra | Jordan normal form | Local ring | Matrix multiplication | Matrix (mathematics) | Length of a module | Abelian group | Module (mathematics)