Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 562 页 · Appendix B，Section B.7「Noetherian and Artinian modules and rings」
An $A$-module $M$ is called Artinian if any non-empty subset of submodules of $M$ has a minimal element (equivalently, every descending chain $N_0\supseteq N_1\supseteq\cdots$ of submodules becomes stationary). The ring $A$ is called noetherian (resp. Artinian) if $A$ as an $A$-module is noetherian (resp. Artinian).