The length of all composition series of a module 
. According to the Jordan-Hölder
theorem for modules, if 
has any composition series,
then all such series are equivalent. The length of a module without composition series
is conventionally set equal to 
.
A module has finite length iff it is both Artinian and Noetherian; this includes the case where
is finite.
An abstract vector space has finite length iff it is finite-dimensional, and in this case the length coincides with the dimension.
