代数数域

嵌入定理与代数数域上的大筛法

Imbedding theorems and the large sieve method in algebraic number fields

代数数域中的均值定理

The mean value theorem in algebraic number fields

有理数域Q的有限次扩域K叫作代数数域，数域K的所有代数整数构成一个环，称为K的代数整数环，记作ZK。

The finite extension K of Q is called algebraic number field .

主要把欧拉函数推广到全矩阵环M（Ok，n）上，其中Ok为代数数域K的整数环。

The Euler function is generalized over the full matrix ring M ( Ok , n ), where Ok is the integral number ring of the algebraic number field K.

代数数域上多项式的一个性质和Heisenberg群上算子的局部可解性

A Property of Polynomials with Coefficients Being Algebraic Numbers and Its Application to Local Solvability on the Heisenberg Group

用实数卷积计算代数数域上整数卷积

On the calculation of integer 's cyclic convolution over algebraic number fields

两类代数数域的化简

The reduction of two classes of algebraic number field

关于代数数域的扩张次数

On the Degree of Extensions of Algebraic Number Field

代数数域上的指数和的估值

On exponential sums over an algebraic number field

多项式与一类代数数域域元素的判别式的闭形式

Closed Form of Discriminants about Elements of Some Type of Algebra Fields and Polynomials

还证明了很多有限次代数数域不与上述的超积初等等价。

Also , it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts .

然后着重在代数范围内进行讨论，得到下列的结果：每个有限次实代数数域都不是归纳域；

Then he considers the case of algebraic numbers and obtains some results like the following : Every real algebraic number field of finite degree is non-inductive ;