Noetherian

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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 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.

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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