素数在某一类四次域中的分解  

The Factorization of Primes in a Quartic Field

作　　者：李江华[1] 姚钟磊[1] 郑金亮[1] 

机构地区：[1]安徽大学数学科学学院,合肥230039

出　　处：《合肥学院学报（自然科学版）》2009年第2期15-18,25,共5页Journal of Hefei University :Natural Sciences

摘　　要：首先确定了四次方程Fa(x)=x4+2(1-a)x2+(1+a)2在Z[x]中可约的充要条件;然后在Fa(x)不可约的前提下,当p为奇素元且p不整除D(f)时,D(f)为Fa(x)的判别式;最后详细论述了p在Fa(x)的根所确定的四次域中的分解情况,并且找出了Fa(x)的根系及它所确定的伽罗瓦群.The reducible condition, which is necessary and sufficient for quartic equation Fα （x） = x^4 ＋ 2（ 1 - α ） x^2 ＋ （1 ＋ α）^2 in Z[ x ] , was confirmed. Under the irreducible precondition of Fα（x）, when p is odd prime and does not divide D（f）, D（,f） will be the discriminant of Fα（x）. The factorization of odd prime in the quartic field was discussed and the roots of Fα （x） and its Galois group were chased down.

关 键 词：素数分解 四次方程 伽罗瓦群 

分 类 号：O152.8[理学—数学]