Eisenstein判别法的推广

On Extension Of Eisenstein's Criterion

证明了:若f(x)=a_nx^n+...+a_1x+a_0是一个整系数多项式,s<n/2为非负整数,如果f(x)在Q上无次数≤s的不可约因式且至少有一种方法可以选取素数ρ,适合ρ(?)a_(n-s),ρ│a_i(0≤i<n—s)且ρ~2(?)a,那么多项式f(x)在有理数域Q上不可约,;因而推广了Eisenstein判别法.

<ABSTRACT> In this paper,it is proved that if f(.x) = anxn+…-a1x+ a0 be a integralploynomial while s <n/2 be a non-negative integral number,and if / (x) has noirreducible factor of degree son Q and at least has a method to select prime number p,with p an-s,p|ai(0≤i<n-s) and p2 a0,then the ploynomial is irreducible on Q. This has developed Eisentein's criterion.