【摘要】 证明了:若f（x）=a_nxⁿ+...+a₁x+a₀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ρ²（?）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.更多还原

【Abstract】 <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.更多还原