@article{Mikhailov2000IntegrableOO,
title={Integrable ODEs on Associative Algebras},
author={A. Mikhailov and V. V. Sokolov},
journal={Communications in Mathematical Physics},
year={2000},
volume={211},
pages={231-251}
}

Abstract: In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our componentless approach we have solved a number of classification problems for integrable equations… CONTINUE READING