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Journal of Siberian Federal University. Mathematics & Physics, 2016, Volume 9, Issue 4, Pages 443–448
DOI: https://doi.org/10.17516/1997-1397-2016-9-4-443-448 (Mi jsfu503) 		 
The determinants over associative rings: a definition, properties, new formulas and a computational complexity

Georgy P. Egorychev

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
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DOI: https://doi.org/10.17516/1997-1397-2016-9-4-443-448
Abstract: 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, noncommutative variables, the polarization theorem, polynomial identities.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00707_a
The research supported by the grant RFFI the project 16-01-00707.
Received: 17.06.2016
Received in revised form: 05.07.2016
Accepted: 15.09.2016
Bibliographic databases:
Document Type: Article
UDC: 512.64+512.55
Language: English
Citation: Georgy P. Egorychev, “The determinants over associative rings: a definition, properties, new formulas and a computational complexity”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 443–448
Citation in format AMSBIB
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\by Georgy~P.~Egorychev
\paper The determinants over associative rings: a definition, properties, new formulas and a computational complexity
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 4
\pages 443--448
\mathnet{http://mi.mathnet.ru/jsfu503}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-4-443-448}
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