研究了正则环上投射根的性质。
We study the properties of projective radicals of regular rings.
由，还证明了分离的阿贝尔正则环是APT环。
By, we prove that a separative Abelian regular ring is an APT ring.
本文给出了分别由约化环类和s -弱正则环类确定的上根的一些基本性质。
Some basic properties of the upper radicals determined by the classes of reduced rings ands-weakly regular rings are presented respectively.
主要对正则环的相关理论进行了研究，包括正则环理想上的模比较，并进一步研究了强正则环的模刻画。
The paper has researched module comparability theories about regular rings, including the module of regular rings and characterizations about modules over strongly regular rings.
研究了每一个极大的右理想是拟理想的右SF -环的正则性，得到了右SF -环是正则环的一些新的刻画，推广了一些已知的结论。
We study the regularity of right SF-rings whose every maximal right ideal is a quasi-ideal. Some new characterizations on the regularity of right SF-rings are obtained, which generalize some results.
再者，引进了分次半平坦模的概念，并有如下主要结果：环K是分次弱正则的当且仅当所有右K-模是分次半平坦的。
Next, the concept of graded semiflat module is introduced and proved that K is a group-graded weakly regular ring if and only if all right K-module is graded semiflat module.
利用环中的群元素刻画了环的单位正则性。
In this paper, we investigate unit regularity by virtue of group members in regular rings.
同时，讨论了一类M -完全正则半环的坚固构架结构。
At the same time, we investigate the sturdy frames of M-completely regular semirings.
研究了一类广义正则半环S上的半环同余。
The semiring congruence on a class of generalized regular semiring S was studied.
第二章，主要研究极大本质单边理想是广义弱理想的SF -环的正则性。
In the second chapter, we study the regularity of SF-rings whose every maximal essential one-sided ideal is generalized weak ideal.
第二章，主要研究极大本质单边理想是广义弱理想的SF -环的正则性。
In the second chapter, we study the regularity of SF-rings whose every maximal essential one-sided ideal is generalized weak ideal.
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