整闭包

Computing integral closure of a finite extension is not only an important problem in commutative algebra, but also in algebraic geometry and algebraic number theory.

计算有限扩张的整闭包不但是交换代数中的一个核心问题，也很受代数几何以及代数数论发展的推动。

The ring C is called the integral closure of A in B.

环C叫作A在B中的整闭包。

In this paper,we give the representation of integral closure of a cubic extension about general Neotherian unique factorization domain (2,3 are not units). Then we give a series of integral number about a cubic extension.

本文在前人研究的基础上，去掉2，3可逆的这一条件，给出了诺特唯一分解环上的三次扩张的整闭包的描述，并由此刻画了一批该扩张下的整元。

Let OKbe the integral closure of the polynomial ring A = Fq in K, and UK be the group ofunits of OK .

设OK为多项式环A = Fq在K中的整闭包， UK为OK的单位群。

In chapter 4, Based on the orthogonality relations and duality of C-algebras, we study the decompositions of C-algebras, and give a Fourier inversion formula on C-algebras, which generalizes the Fourier inversion formula on the center of a finite group algebra over complex. As an application, we characterize the integral closure of C-algebras over the ring of integers, and show a necessary and sufficitient condition for elements of C-algbras being algbraic integral over integers.

第四章 我们应用C-代数的正交性及对偶性刻画了C-代数的一个分解，给出了C-代数上这个完全分解的Fourier反演公式，从而推广了Z分解的Fourier反演公式；作为Fourier反演公式的一个应用，我们刻画了Z在整数环Z上的整闭包，进一步我们研究了C-代数在整数环Z上的整闭包，给出了C-代数在整数环Z上为整元的一个充要条件。

Neotherian unique factorization domain; cubic extension; integral closure

诺特唯一分解环；三次扩张；整闭包

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。