English Dictionary

Noetherian ring

IPA（発音記号）

/nə.ˈtɛ.ɹi.ən ˈɹɪŋɡ/

名詞

(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).

日本語の意味

（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。

When working with modules over a Noetherian ring, many ascending chains of submodules stabilize, which makes classification problems more tractable.

イデアルがすべて有限生成される環上の加群を扱うとき、多くの部分加群の上昇鎖は安定し、分類問題がより扱いやすくなります。

意味（1）

(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).

The central position occupied by Noetherian rings in commutative ring theory became evident from her work.

Noetherian rings （ plural ）