Concept

Noetherian

Summary
In mathematics, the adjective Noetherian is used to describe that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite length. Noetherian objects are named after Emmy Noether, who was the first to study the ascending and descending chain conditions for rings. Specifically:
  • 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.
  • More generally, an object in a is said to be Noetherian if there is no infinitely increasing filtration of it by subobjects. A category is Noetherian if every object in it is Noetherian.
  • Noetherian relation, a binary relation that satisfies the ascending chain condition on its elements.
  • Noetherian topological space, a topological space that
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