An -module is Noetherian when every submodule is finitely generated, equivalently when every ascending chain of submodules stabilizes. Quotients and finite direct sums of Noetherian modules are Noetherian.
In abstract algebra, specifically in the context of module theory, a **Noetherian module** is a module that satisfies the ascending chain condition on its submodules. This means that every increasing chain of submodules eventually stabilizes.
New to topics? Read the docs here!