Examples
The zero module is the only one with length 0. Modules with length 1 are precisely the simple modules.
For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide.
The length of the cyclic group Z/nZ (viewed as a module over the integers Z) is equal to the number of prime factors of n, with multiple prime factors counted multiple times.
Read more about this topic: Length Of A Module
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