2型_(χ^-)CS模的直和

Direct Sums of 2 Type _(χ^-)CS Modules

通过讨论 2型 χ CS模的直和是 2型 χ CS模 ,可以证明 :对任意直和M = i∈IMi是 2型 χ CS模的充要条件是在I中存在i,j,满足i≠ j,对于M的任意一个闭子模K ∈ χe(M ) ,若K ∩Mi =0或K ∩Mj =0 ,则必有K｜M 此外 ,还考虑了当M是UC模时 ,M是 2型 χ

This paper is concerned with when a direct sum of 2 type χ CS modules is a 2 type χ CS module. For example, it is proved that the direct sum M= i∈I M i is 2 type χ CS module if and only if there exists i≠j in I such that every closed submodule K of M with K∈χ e(M),K∩M i=0 or K∩M j=0 is a direct summand. In addition, when M is UC module, it is considered with when M is 2 type χ CS module.