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.
![R](/Images/godic/202502/04/e1e1d3d40573127e9ee0480caf1283d64337.png")
的理想![I](/Images/godic/202502/04/dd7536794b63bf90eccfd37f9b147d7f4337.png")
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\}](/Images/godic/202502/04/e376596c684d68b046cc29a219a6a1414337.png")