A note about algebric integer and algebra number
Cheng Liang-yun · Journal of Northeast Normal University · 2011
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.