关于代数整数与代数数的一个注记

A note about algebric integer and algebra number

证明了代数数是有理数系数方阵的特征值,代数整数是整数系数方阵的特征值.由此出发,完全用线性代数与矩阵计算的方法简洁地证明了代数整数对加减法和乘法封闭,从而构成一个环(代数整数环);所有代数数对加减乘除封闭,从而构成一个域(代数数域).

In this paper,it is proved that an algebraic number can be seen as an eigenvalue of a matrix over rational field,and an algebraic integer can be seen as an eigenvalue of a matrix over integral ring.Then the important conclusion in mathematics that all algebraic integers form a ring and the field of its fractions is an algebraic number field is directly and clearly proved,in history the prove of this conclusion is much difficult for people to understand.