1Of, relating to, or arising from the work of Max or Emmy Noether.
2Specifically. Designating a ring in which there exists no infinitely growing sequence of ideals such that each ideal is a subset of the next in sequence. Also: designating a module in which there exists no infinitely growing sequence of submodules such that each is a subset of its successor.
Early 20th century; earliest use found in American Journal of Mathematics. From Noether, the family name of two German mathematicians, Max Noether, and his daughter Emmy (Amalie) Noether, who developed her father's work and described the class of rings named after her in 1921 (Math. Ann 83 24–66) + -ian.