Gauss整数的既约分解

THE IRREDUCIBLE DECOMPOSITION OF GAUSS INTEGRAL NUMBER

Gauss整数环Z[i]是单一分解整环。因而任一Gauss整数Z=a+bi(a、6∈Z)都可以分解为既约元的乘积。此文首先给出Gauss整数环Z[i]的既约元与其范数的关系,Z[i]的既约元的集合,然后讨论素(自然)数在Z[i]中的既约分解。在以上基础上给出Gauss整数的分解方法。

Gauss integral ring Z(i) is a unique facterization domain, so any Gauss integral numebr Z=a+bi (a, bEZ) can be decomposed to a product of the irreducible element. This thesis first sheds light to the relations between the irreducible element of Gauss integral ring Z(i) and its norm, the gathering of the irreducible elements of Z(i) and the irreducible decomposition of prime in Z(i), and, on the basis of these, puts forward a method of decomposition of Gauss integral.