Editing Noetherian module (section)

==Examples==
*The [[integer]]s, considered as a module over the [[ring (mathematics)|ring]] of integers, is a Noetherian module.
*If ''R''&nbsp;=&nbsp;M<sub>''n''</sub>(''F'') is the full [[matrix ring]] over a field, and ''M''&nbsp;=&nbsp;M<sub>''n'' 1</sub>(''F'') is the set of column vectors over ''F'', then ''M'' can be made into a module using [[matrix multiplication]] by elements of ''R'' on the left of elements of ''M''. This is a Noetherian module.
*Any module that is finite as a set is Noetherian.
*Any finitely generated right module over a right [[Noetherian ring]] is a Noetherian module.