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单词 Principal ideal
释义

Principal ideal

中文百科

主理想

在抽象代数里,环R的理想I称为主理想(principal ideal),若

\exists\, a \in R: I = RaR = \left\{ \sum_{i=1}^n r_ias_i: n \in \mathbb{N}, r_i, s_i \in R \,\forall\, i \right\}

如果R所有的理想都是主理想,则R称为主理想环。

英语百科

Principal ideal 主理想

In the mathematical field of ring theory, a principal ideal is an ideal I in a ring R that is generated by a single element a of R through multiplication by every element of R. The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset P generated by a single element x of P, which is to say the set of all elements less than or equal to x in P.

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更新时间:2025/6/20 6:59:48