A non-Artinian module consists of an infinitely descending chain.
An Artinian module is one that satisfies the following descending chain
condition: A module B is said to satisfy the descending chain condition
if for every chain B1> B2 >B3> ... > Bn> Bn+1>... of submodules of B, there is an integer m such that Bi=Bm for all i > m. (Hungerford)
|