中文摘要：

引进了余因子系的概念，并利用余因子系给出一种惟一分解环上多项式系公因子存在性的分次判别准则，为在计算代数几何等领域的深入应用提供了理论依据．

英文摘要：

The theory about common factor of polynomials is very important in many research fields,such as symbolic computation, interpolation theory, automatic theorem proving, and robotics. This paper introduces the cofactor system of a polynomial system on unique factorization domain. Using the cofactor system, it obtains a criterion on common factor with given arbitrary degree. This result provides a theory foundation of application in computational algebraic geometry and other corresponding fields.