2017
Том 69
№ 6

All Issues

Theorem on elementary divisors for a ring of differential operators

Kazimirskii P. S.

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Abstract

This paper presents the proof of the following theorem:
For any matrix with elements of a differential ring $\Delta_{\tau}$ from $n$ differentiations there exist such reversible over $\Delta_{\tau}$ matrices $P$ and $Q$ for which relationship (1) holds.
If the matrix $A$ is of quadratic order and rank $n$ then (1) has the form of (2).

Citation Example: Kazimirskii P. S. Theorem on elementary divisors for a ring of differential operators // Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 309-318.

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