Some equivalent conditions of left hereditary rings and left subhereditary rings are given,and the direct sum of left subhereditary rings is discussed.
给出了左遗传环、左亚遗传环的几个等价条件,讨论了左亚遗传环的直和,还讨论了左亚遗传环与SI-环、半单环的关系。
Moreover, we prove Noether N-semisimple rings are a kind of rings that lie between semisimple rings and left hereditary rings.
本文引入了N-投射模、N-内射模的概念,由此构造了一种环,称为N-半单环,并且证明出NoetherN-半单环是介于半单环与左遗传环之间的一种环。
Noether N-left hereditary rings;
Noether N-左遗传环
Some equivalent conditions of left hereditary rings and left subhereditary rings are given,and the direct sum of left subhereditary rings is discussed.
给出了左遗传环、左亚遗传环的几个等价条件,讨论了左亚遗传环的直和,还讨论了左亚遗传环与SI-环、半单环的关系。
Then we introduce left maximal P hereditary ring and characterize it by maximal P-injective modules.
引进了极大P-内射模的概念,讨论了它的一些基本性质及其在整环上的特殊性质;其次引进了左极大P遗传环,并用极大P-内射模对它进行刻划。