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.
本文讨论非交换分次环上的纲性分次自对偶与其初始子环上的自对偶之间的关系。
In this paper, we discuss the connection between the rigid graded selfduality over some noncommutative graded ring and the selfduality over its initial subring.
同时对盟定义了盟模，并证明了对部分半群g，所有G -盟作成的范畴与所有G -分次环作成的范畴是同构的。
It is proved that for a partial semigroup g, the category of G-unions and the category of G-graded rings are isomorphic.
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.
第一章中，我们研究了剩余域是代数闭域的离散赋值环上的完全分次代数；
In the first chapter, we discuss the fully graded algebras over discrete valuation ring with an algebraically closed residue field of characteristic p.
第一章中，我们研究了剩余域是代数闭域的离散赋值环上的完全分次代数；
In the first chapter, we discuss the fully graded algebras over discrete valuation ring with an algebraically closed residue field of characteristic p.
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