模的r-比较与r-幂比较  

The r-Comparability and r-Power Comparability of Modules

作　　者：黎奇升[1] 佟文廷[2] 

机构地区：[1]吉首大学数学与计算机科学学院,吉首416000 [2]南京大学数学系,南京210093

出　　处：《数学学报（中文版）》2007年第3期567-576,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10071035);湖南省自然科学基金(03JJY6017);吉首大学博士基金

摘　　要：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.

关 键 词：r-比较 r-幂比较 置换环 可分性 

分 类 号：O153.3[理学—数学]