Page "Indecomposable module" Paragraph 16

For a fixed positive integer n, consider the ring R of n-by-n matrices with entries from the real numbers ( or from any other field K ).

Then K < sup > n </ sup > is a left R-module ( the scalar multiplication is matrix multiplication ).

This is up to isomorphism the only indecomposable module over R. Every left R-module is a direct sum of ( finitely or infinitely many ) copies of this module K < sup > n </ sup >.