Let be a ring and let be a (right or left) -module. A series of submodules
A module need not have a composition series. For example, the ring of integers, , considered as a module over itself, does not have a composition series.
If a module does have a composition series, then all composition series are the same length. This length (the number above) is called the composition length of the module.
If is a semisimple Artinian ring, then and always have composition series.
|Date of creation||2013-03-22 14:04:13|
|Last modified on||2013-03-22 14:04:13|
|Last modified by||mclase (549)|