• Noetherian

FromEmmy Noether.

• IPA^(key):/noʊˈθɪəriən/

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noetherian (notcomparable)

1. (algebra) Satisfying some (usuallyascending)chain condition:
   2. (of aring) In which any ascending chain ofideals eventually becomes constant.
   3. (of amodule) In which any ascending chain ofsubmodules eventually becomes constant.
   4. (of agroup) In which any ascending chain ofsubgroups eventually becomes constant.
   5. (of atopological space) In which any ascending chain ofopensubsets eventually becomes constant.
2. (mathematics, of abinary relation on aset) Such that theconverse relation iswell-founded (on that set).
3. (algebraic geometry, of ascheme)admitting afinite covering by openaffine subsets${\displaystyle \mathrm{Spec}{A}_i}$, where each${\displaystyle A_i}$ is anoetherian ring;

• Artinian
• ascending chain condition

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