给出了两两互素多项式下线性变换的核的直和分解，并应用于幂等矩阵（对合矩阵）的秩的等式证明中。

The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given, and it was used in the proof of some equality about the rank of idempotent matrix.

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利用矩阵的秩给出一元多项式整除性的判定定理，同时给出商式的简便求法。

This text that make use of the order of matrix gives outs the unitary polynomials divide exactly theorem of judgment; And give a simple and convenient method about quotients type at the same time.

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