Editing Length of a module (section)

==== Artinian modules over Z ====
The length of the [[cyclic group]] <math>\mathbb{Z}/n\mathbb{Z}</math> (viewed as a module over the [[integer]]s '''Z''') is equal to the number of [[prime number|prime]] factors of <math>n</math>, with multiple prime factors counted multiple times. This follows from the fact that the submodules of <math>\mathbb{Z}/n\mathbb{Z}</math> are in one to one correspondence with the positive divisors of <math>n</math>, this correspondence resulting itself from the fact that <math>\Z</math> is a [[principal ideal ring]].