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.

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