模的弱消去问题与qu－正则环

Weak Cancellation of Modules and qu-Regular Rings

本文考虑模的弱消去问题与正则环的Ｓｔａｂｌｅｒａｎｇｅ条件，引进了ｑｕ－正则环的概念，并用它刻划了一类满足弱消去条件的模，刻划了ｑｕ－正则环，指出一切满足比较公理的正则环均为ｑｕ－正则环．文中还考虑这些结果的应用．例如，刻划了满足弱消去律的拟内射模；证明了素的正则右自内射环上的任意非奇异内射右Ｒ－模可以从直和项中弱消去．

This paper studies weak cancellation of niodules and stable range condition of regularrings.We introduce the concept of qu-regular rings and apply it to characterizing a class ofmodules satisfying weak cancellation. We characterize qu-regular rings and indicate that allregular rings satisfying comparability axiom are qu-regular.We also consider the applicationsof these results,e.g.,we characterized quasi-injectiVe modules satisfying weak cancellation;weproved that every nonsingular injective right R-module over a prime,regular and right self-inective ring R can be weakly cancelled from direct summands.