类似于群分次环和群分次模的定义，定义了部分半群分次环和部分半群分次模。
Similar to group graded rings and modules, partial semigroup graded rings and modules are defined.
对一般群分次环建立了弱分次周期根的概念，证明它是一个分次特殊根，给出了它的分次模刻划，讨论了它与自反周期根的关系。
The weakly graded periodic radical concept for general group graded rings is established, the fact that it is a graded special radical is proved and its graded module characterization is presented.
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.
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