两类域的结构

The Structure of Two Kinds of Field

本文证明了①域（Ｆ；＋，·，０，１）的任一非零加法子群皆为子域域Ｆ≌Ｚ＿ｐ（Ｐ为素数），②域（Ｆ；＋，·，０，１）的任一乘法子群皆为某子域的乘法群域Ｆ≌Ｚ＿２，或Ｚ＿２（ａ），且ａ的阶数ｏ（ａ）＝素数ｐ，｜Ｆ｜＝ｐ＋１。

In this paper, the author proved two theorems,① If H is a additionsubgroup of field F, and H≠{0},then H is a subfield of( P is a primenumber;②If M is a multiplication subgroup of field F, then M∪{0} is a subfield of(o(a)=p p is a prime number), or Z_2, and when, F|=p+1.