English Dictionary

maximal ideal

名詞

(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).

日本語の意味

環論や代数学において、これ以上大きな適正な（部分的な）イデアルに拡大することができない、つまり追加の要素を加えると全体（環全体など）になってしまうイデアル。

Every maximal ideal in a commutative ring corresponds to a field when we take the quotient by that ideal.

可換環における極大イデアルは、そのイデアルで商を取ると体に対応する。

意味（1）

(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).

Denote the minimal prime ideal in (b) by J_ mathsf max(𝜆), the unique maximal ideal of infinitesimal character 𝜆.

maximal ideals （ plural ）