Definition
Let M be a (left or right) module over some ring R. Given a chain of submodules of M of the form
we say that n is the length of the chain. The length of M is defined to be the largest length of any of its chains. If no such largest length exists, we say that M has infinite length.
A ring R is said to have finite length as a ring if it has finite length as left R module.
Read more about this topic: Length Of A Module
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