摘要
In this paper, we give the concept of relative hereditary ring and charac-terizatin of relative hereditary ring. The relations between relative hereditary rings, semi-hereditary rings and hereditary rings are studied. Finally, we prove that end-morphism rings of left ideal of some relative hereditary rings and endmorphism rings of finitely generated relative projective modules over some relative hereditary rings are semi-hereditary rings.
本文给出了左相对遗传环的概念及刻划.讨论了左相对遗传环与左遗传环,左半遗传环的关系,并给出了左遗传环的几个新的刻划.最后,证明了左相对遗传环(相对于左模范畴的生成元)的左理想的自同态环是左半遗传的;左相对遗传环(相对于左模范畴的内射生成元)上的有限生成相对投射模的自同态环是左半遗传的等结果.
