分式格的理想与格的局部化

On the Ideals of Fractional Lattice and the Localization of Lattice

本文在〔1〕的基础上讨论分式格的理想及格的局部化问题。主要结论是:1°记分配格L对于其交闭子集S的分式格为S^(-1)L,则S^(-1)L中任一理想可表示为S^(-1)I=Φ.(I)的形式,其中I是L的某个理想,是格(满)同态。2°若P是分配格L的素理想,则L在P的局部化L_p只含有唯一极大理想(局部格)。最后,给出格的局部化的一个例子。

In this paper , we discuss the structure of the ideals of fractional lattice and the localization of lattice based on [1] .The main results are the following.1·Every ideal in S-1L can be expressed by the form of φ3(I) , where φ3: L→ S-1L(r→r/s) is a homormophism and I is an ideal ot L.2? If P is a prime ideal of a distributive lattice, then S=L-P is an interse-ctive subset or L, and the localization or L on P(S-1L)has the unique maximal ideal.At the end ot this paper, an example of the localization ot lattice is given.