多项式环Z_(p^e)[x]中的Hensel引理及提升

Hensel′s lemma and lift in the polynomial ring Z_(p^e)[x]

在多项式环 Zpe[x]中 ,建立了 Hensel引理及提升 ,并利用 Hensel引理证明了 xn- 1在 Zpe[x]中可惟一分解成基本不可约多项式的乘积 ,其中 (n,p) =1。

In the polynomial ring Z p e , the Hensel′s lemma and lift are given. Moreover, it is proved that the polynomial x n-1, where (n,p)=1, can be uniquely factored into a product of finitely many pairwise coprime basic irreducible polynomials in Z p e .