noetherian

Adjective

not-comparable

(algebra) Of a ring in which any ascending chain of ideals eventually starts repeating. / (algebra) Of a module in which any ascending chain of submodules eventually starts repeating.

Japanese Meaning

代数において、環が任意の冪増加するイデアルの鎖において最終的に反復（安定）する性質を持つこと。 / 代数において、加群が任意の冪増加する部分加群の鎖において最終的に反復（安定）する性質を持つこと。

What is this buttons?

To prove the theorem, she assumed the base scheme was noetherian, which simplified the control of its ideals.

Google Translation / DeepL Translation

定理を証明するために、彼女は基底スキームがイデアルに関する任意の増大鎖が最終的に安定する環であると仮定し、それによってイデアルの扱いが容易になった。

Details

Sense（1）

(algebra) Of a ring in which any ascending chain of ideals eventually starts repeating.

Sense（2）

(algebra) Of a module in which any ascending chain of submodules eventually starts repeating.

Details

noetherian

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