Geodesic
The determinants over associative rings: a definition, properties, new formulas and a computational complexity
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 443-448

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We give a new definition for the determinants over an associative ring $\mathbf{Q}$ and study their properties. In particular, we obtain a new family of polynomial identities (computational formulas) for these determinants that contain up to $n!$ free variables.
Keywords: determinants, associative rings, the polarization theorem, polynomial identities.
Mots-clés : noncommutative variables 
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     title = {The determinants over associative rings: a definition, properties, new formulas and a computational complexity},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Georgy P. Egorychev. The determinants over associative rings: a definition, properties, new formulas and a computational complexity. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 443-448. http://geodesic.mathdoc.fr/item/JSFU_2016_9_4_a4/