Indecomposable module
= Indecomposable module
A nonzero <module> is indecomposable if it cannot be expressed as a <direct sum> of two nonzero <submodules>. The zero <module> is excluded. A <module> of finite <composition length> is indecomposable exactly when its <endomorphism ring> has no <idempotents> other than zero and one: an <idempotent> splits the <module> into its image and <kernel>.