环范畴

研究结合环范畴中的半遗传对偶根，证明了如果存在一个特征为零的单环是一个R-根环，则半遗传对偶根R是一个遗传根；

The semihereditary radical was studied , it is proved that a semihereditary dual radical R is hereditary if there exists a simple ring of characteristic zero such that it is an R & radical ring .

在环范畴的子范畴间定义了四元数函子，并证明了它是一个正合函子，同时讨论了环类的遗传性，同态闭性在四元数函子下的变化情况。

We defined the quaternion functor Q on rings categories , and proved that Q is an exact functor .

环上模子范畴间的等价与对偶

Equivalence and Duality between Sub - Categories of Modules

仅有局部单位元环上的范畴对偶

Dull for Categories with only Local Units

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 .

设H为有限Hopf代数，B为交换环，H0为交换、余交换的有限Hopf代数范畴，C为交换环范畴，A为交换群范畴。

Let H be a finite Hopf algebra , B a commutative ring , H 0 the category of all commutative , co-commutative finite algebra , C the category of commutative rings and A of commutative groups .