Abstract

We investigate the connection between divisibility of full-rank square matrices of linear scalar differential operators over some differential field K, and the solution spaces of these matrices over the universal Picard–Vessiot extension of K. We establish some properties of the solution spaces of the greatest common right divisor and the least common left multiple of such matrices.

中文翻译：

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标量微分算子矩阵：可分性和解的空间

摘要

我们研究了线性标量微分算子的全秩平方矩阵在某些微分场K上的可除性与这些矩阵在K的普遍Picard-Vessiot扩展上的解空间之间的联系。我们建立了此类矩阵的最大公右因数和最小公左因数的解空间的一些性质。