主弱n-平坦系的有向上极限与直积

摘要

Let n be any positive integer.The article prove principally weakly n-flat S-acts are closed under directed colimits,and give a sufficient and necessary condition over which the direct products of principllay weakly n-flat S-acts are principally weakly n-flat.As application,some known results are generalized.%设n是任意正整数.证明了主弱n-平坦系关于有向上极限封闭,并且给出了主弱n-平坦系的任意直积仍然是主弱n-平坦系的充分必要条件.作为应用,推广了一些已有的成果.