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.

UDC: 512.64+512.55

Received: 17.06.2016
Received in revised form: 05.07.2016
Accepted: 15.09.2016

Language: English

DOI: 10.17516/1997-1397-2016-9-4-443-448

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