Last Updated
：2025/11/28
Noetherian domain
IPA(Pronunciation)
Noun
Japanese Meaning
整域かつノエタリア環。すなわち、上昇鎖条件（全てのイデアル系列が安定するという条件）を満たす環のうち、零因子が存在しない（0でない元同士の積が0にならない）性質を持つ環。
（ plural ）
Quizzes for review
A Noetherian ring which is also an integral domain.
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Noetherian domain
When studying algebraic geometry, it is often convenient to assume the coordinate ring is a Noetherian domain to apply finiteness results.
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When studying algebraic geometry, it is often convenient to assume the coordinate ring is a Noetherian domain to apply finiteness results.
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