【摘要】 利用可除模的可除性和延拓性,展开了可除模对一些环的刻画.在给出了有关可除模的主要性质后,定义PR-内射环和SD-环,并得到这两类环的几个等价的特征.最后利用可除模、平坦模和其他几类具有延拓性质的模之间的关系来研究Von Neumann正则环和半单环.更多还原

【Abstract】 In this paper,we characterize some kinds of rings through the divisiblity and continuability of the divisible modules.After giving the main conclusion of the divisible modules,we define PR-injective rings and SD-rings.We obtain some equivalent characterization of two kinds of rings.Finally,we study Von Neumann regular rings and semisimple rings by investigating the relations among divisible modules,flat modules and other four kinds of modules with extending properties.更多还原