构造整数环上的一类不可约多项式

Constructing Some Irreducible Polynomails in Integral Ring

介绍了满射多项式的基本性质,证明了:当n≥5时,对任何S0Z且|S0|=n,有E(S0,T0)=Φ.由此得到了如何构造Z[x]中的一类不可约多项式的方法:设φ(x)∈Z[x]是Z上无重根完全可约的多项式且次数大于等于5,若二次整系数多项式f(x)∈Z[x]在有理数域Q上不可约,则f(φ(x))在Q上不可约.

This paper introduces some basic properties on epimorphic polynomial. And it is concluded that if n ≥ 5 then for any S0 lohtain in Z with ｜ S0 ｜ = n, E（S0. r0） = Ф. Furthermore, a method of constructing some irreducible polynomials in Z [x] is obtained： suppose φ（x）E Z[x] with degree≥5 and all its roots are different integral from each other, f（φ（x）） is irreducible on Q whenf（x）EZ[x] is irreducible on Q with degree equals 2.