On Hyperdeterminants And Equations Over Noncommutative Rings

Main Article Content

Nino Tophuridze
Giorgi Rakviashvili


The main goal of the paper is to investigate some features of polynomials and hyperdeterminants over noncommutative rings, namely over quaternion skew-field and division rings with involution; these results generalized well-known results of A. Cayley, I. Gelfand, M. Kapranov, A. Zelevinsky, X. Zhao, Y. Zhang and others. Main results are: the estimation of number of roots of canonical polynomials over quaternions – they are infinite unlike number of roots of polynomials over real field and generalization of results of X. Zhao, Y. Zhang on resultants and its features of polynomials over quaternions to polynomials over division rings with involution (Theorems 2-5). Also, in last paragraph of the paper is hypothesized what form should it be the cubical hyperdeterminant of order three over division ring with involution.

Quaternions resultant noncommutative hyperdeterminants division rings with involution
Published: Nov 21, 2021

Article Details

How to Cite
Tophuridze, N. ., & Rakviashvili, G. . (2021). On Hyperdeterminants And Equations Over Noncommutative Rings . Proceedings of Tskhum-Abkhazian Academy of Sciences, 21, 158–166. Retrieved from https://proceedings.taas.ge/index.php/taas/article/view/5445
Pure Mathematics
Author Biographies

Nino Tophuridze, Sokhumi State University

Doctor of Mathematics

Associate Professor of Sokhumi State University

E-mail: ntophuridze@sou.edu.ge

Giorgi Rakviashvili, Ilia State University

Doctor of Mathematics

Ilia State University

E-mail: giorgi.rakviashvili@iliauni.edu.ge