模的r-比较与r-幂比较

The r-Comparability and r-Power Comparability of Modules

本文研究模的r-比较性和r-幂比较性,给出了r-比较性的新刻划,得到了模的r-幂比较结构与其自同态环的r-幂比较性间的关系,证明了如果模M为r-幂比较的则它的任意直和项也是r-幂比较的．对于可分置换环,给出了r-幂比较性与r-比较性间的联系．

This paper concerns the related comparability and related power comparability of rings and modules, and some new characterizations for the related comparability are given. The relations between the related power comparability of rings and the related power comparable structures of modules are obtained. It is shown that if a module M has the related power comparability then so does each direct summand of M. For a separative exchange ring R, we further give the connections between the related comparability and the related power comparability.