Noetherian

In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects; in particular,

• Noetherian group, a group that satisfies the ascending chain condition on subgroups
• Noetherian ring, a ring that satisfies the ascending chain condition on ideals.
• Noetherian module, a module that satisfies the ascending chain condition on submodules.
• Noetherian topological space, a topological space that satisfies the descending chain condition on closed sets.
• Noetherian induction, also called well-founded induction.
• Noetherian rewriting system, an abstract rewriting system that has no infinite chains
• Noetherian scheme.

See also:

• Emmy Noether, who was the first to study the ascending and descending chain conditions for rings, and for whom the term is named.
• Artinian ring, a ring that satisfies the descending chain condition on ideals.