D算子性质的进一步研究及应用

Further Research and Application of the Properties of D Operator

本文将D算子的定义和性质推广到一般数域上,得到了D算子在最大公因式、矩阵多项式的秩等式以及多项式的可约性等方面的性质,并将已有文献中对多项式不可约的判别法进行推广,丰富了对多项式不可约的判别方法。

This paper extends the definition and characters of D operator to general number field, and obtain the characters of D operator in the greatest common factor, the rank equalities of matrix polynomial and the reduc ibility of polynomial, and generalize the discriminances of polynomial irreducibility in existing literature, enric hing the discriminances to polynomial irreducibility.