In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.
本文在介绍了K〓理论和相对K〓理论以及与K〓理论有关的2阶典型群的基本概念及主要成果之后，对于虚二次域代数整环的K〓群的计算，非GE〓泛的虚二次域的子环以及K〓到K〓的自然同态的余核的生成元集等问题进行了研究。
On the AFS theory, we define a homomorphism mapping between the EI algebra and the ring of Boolean matrix.
在EI代数的子代数的基础上，对概念的EI代数表示和布尔矩阵表示进行了讨论。
At first, we define a ring homomorphism from Z_q to Z_p, and prove that the polynomial x~n-1 over Z_q can be uniquely factored into a product of finitely many pair-wise coprime basic irreducible polynomials over Z_q.
首先，定义一个从Zq到Zp的环的同态，并且证明多项式x~n-11在Zq上能被唯一分解成有限个一些两两互素的基本不可约多项式的乘积。
On the AFS theory, we define a homomorphism mapping between the EI algebra and the ring of Boolean matrix. Some attribute and some new methods of studying the Sub algebra are found out at the same time.
本文在AFS理论的基础上，给出了EI代数和布尔矩阵环之间的一个同态关系，并且找到了子代数的一些性质和研究子代数的新方法。
The concept of fuzzy homomorphism between two near-ring was defined.
本文首先定义了两个拟环之间的模糊同态映射。
The roughness of fuzzy ideals and fuzzy sub-ring and the properties of homomorphism mapping of them
模糊理想和模糊子环的粗糙性及其在同态下的性质
We also discuss some properties and homomorphism basic theorem of generalized ring.
并将环的性质、同态基本定理推广到广义环上，得到了广义环的性质、广义环的同态基本定理。
Making use of the Sander and Tschudin defined homomorphic encryption scheme in the integer ring, we design a new protocol, the homomorphism key agreement.
利用Sander和Tschudin提出的整数环上的同态加密机制，提出了一种新的密钥协定&同态密钥协定。
Then, by choosing an appropriate homomorphism from skew-polynomial ring to the matrix ring, we can get an identity.
作为该恒等式的一个应用，我们适当选取斜多项式环到矩阵环的同态，得到一个恒等式。
Operator Homomorphism of Linear Form Modul over Ring and Matrices
环上线性模的算子同态与矩阵
Fuzzy Homomorphism of Module on Ring
环上模的Fuzzy同态
An Equivalence of Semi - ring Homomorphism and Semi - module
半环同态与半模的一个等价性
At first, we define a ring homomorphism from Z_q to Z_p, and prove that the polynomial x ~ n-1 over Z_q can be uniquely factored into a product of finitely many pair-wise coprime basic irreducible polynomials over Z_q.
首先，定义一个从Zq到Zp的环的同态，并且证明多项式x~n-11在Zq上能被唯一分解成有限个一些两两互素的基本不可约多项式的乘积。
In this part, we mainly focus on some concepts such as integral domain, division ring, field, ideal, difference ring, isomorphism, homomorphism and anti-isomorphism.
本部分主要介绍整区、除环、域、理想、差环、同构、同态及反同态等基本概念。