Geodesic
Non-commutative Hamilton–Cayley theorem and roots of characteristic polynomials of skew maximal period linear recurrences over Galois rings
Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 2, pp. 65-76 
M. A. Goltvanitsa. Non-commutative Hamilton–Cayley theorem and roots of characteristic polynomials of skew maximal period linear recurrences over Galois rings. Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 2, pp. 65-76. http://geodesic.mathdoc.fr/item/MVK_2017_8_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $p$ be a prime number, $R = \mathrm{GR}(q^d, p^d)$, where $q = p^r$, be a Galois ring, $S = \mathrm{GR}(q^{nd}, p^d)$ be its extension. We prove a non-commutative generalization of the well-known Hamilton–Cayley theorem. Using this result we prove the existence of roots in some extension $\mathcal{K}$ of $\check{S}$ for characteristic polynomials of skew maximal period linear recurrent sequences over $S$. Also for these polynomials we investigate the structure of the set of their roots.

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