Last Updated
：2025/11/28
Noetherian ring
IPA(Pronunciation)
Noun
Japanese Meaning
（代数学・環論）すべてのイデアルが有限生成される可換環、または左・右のイデアルがそれぞれ有限生成される非可換環のこと。
（ plural ）
Quizzes for review
(algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated).
音声機能が動作しない場合はこちらをご確認ください
See correct answer
Noetherian ring
When working with modules over a Noetherian ring, many ascending chains of submodules stabilize, which makes classification problems more tractable.
See correct answer
When working with modules over a Noetherian ring, many ascending chains of submodules stabilize, which makes classification problems more tractable.
音声機能が動作しない場合はこちらをご確認ください
English - English
Word Edit Setting
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Sentence Edit Setting
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Quiz Edit Setting
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
