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.
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.
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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