Algebra
Some remarks on non-commutative principal ideal rings
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 5-8.

We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are used in the theory of non-local Poisson structures.

Nous démontrons quelques résultats algébriques sur lʼanneau des matrices dʼopérateurs différentiels sur un corps différentiel dans le cas général des anneaux principaux non commutatifs. Ces résultats sont utilisés dans la théorie des structures de Poisson non locales.

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DOI: 10.1016/j.crma.2013.01.006
Carpentier, Sylvain 1; De Sole, Alberto 2; Kac, Victor G. 3

1 École normale supérieure, 75005 Paris, France
2 Dipartimento di matematica, University of Rome-1, “La Sapienza”, 00185 Roma, Italy
3 Department of Mathematics, M.I.T., Cambridge, MA 02139, USA
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Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G. Some remarks on non-commutative principal ideal rings. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 5-8. doi : 10.1016/j.crma.2013.01.006. http://www.numdam.org/articles/10.1016/j.crma.2013.01.006/

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[3] De Sole, A.; Kac, V.G. Non-local Poisson structures and applications to the theory of integrable systems I, 2012 (preprint) | arXiv

[4] De Sole, A.; Kac, V.G. Non-local Poisson structures and applications to the theory of integrable systems II, 2012 (preprint) | arXiv

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