Noetherian Module
In
ring theory
, if
R
is a
ring
and
M
is a
module
over
R
, then
M
is
Noetherian
if
M
satisfies the
ascending chain condition
on its submodules when they are ordered by inclusion. Noetherian modules are named in honor of
Emmy Noether
. Any finitely generated module over a
Noetherian ring
is a Noetherian module.
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