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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 4, Pages 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

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.


DOI: https://doi.org/10.17516/1997-1397-2016-9-4-443-448

Full text: PDF file (105 kB)
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Bibliographic databases:

UDC: 512.64+512.55
Received: 17.06.2016
Received in revised form: 05.07.2016
Accepted: 15.09.2016
Language:

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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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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