Under some condition,some relations between quasi-quotient rings and weak HX rings are proved.

Some properties of the Gauss integral ring and the quotient ring;

An explicit express of the basis in the dual linear space by the linear space of the quotient ring of the polynomials ring;

The definition and some properties of the quotient ring,the unit and the simple element of Gauss integral ring are discussed,element numbers of the quotient ring of Gauss integral ring is researched,and the forms of unit and two forms of simple element are given.

The algebra systemquasi ring has been further studied by using the quasi group.

In this paper,the author establishes a kind of special ring——the quasi ring by using quasi group, then studies its characteristics and structure, at the same time, obtains a series of results about quasi group.

The commutative theorem characterized by an associative ring, presented in document 1 noted by Guo Huaguang is extended to the formation of the left near ring with partition law.

This paper discusses the basic properties, ideals and quotients of the near rings which meet distributive law, and some important theovems of ring theories were extended into near rings.

The concept of fuzzy homomorphism between two near-ring was defined.

The paper defined two radicals R 0 and R c for near-rings and proved some poperties of these radicals.