Ya.A. Kalinovsky, Yu.E. Boyarinova
Èlektron. model. 2017, 39(3):61-76
https://doi.org/10.15407/emodel.39.03.061
ABSTRACT
A method is presented for determining isomorphism of indecomposable commutative hypercomplex numerical systems through analysis of the representations of exponential functions in these systems. It is shown that this approach greatly simplifies the systems of isomorphism equations.
KEYWORDS
hypercomplex number system, commutativity, isomorphism, exponential function, isomorphism operator, multiplicity of the roots.
REFERENCES
1. Kalinovsky, Ya.A. (2016), “Efficient algorithms for solution of the system of isomorphism equations of hypercomplex number systems with presentation of exponential functions”, Elektronnoe modelirovanie, Vol. 39, no. 1, pp. 75-90.
https://doi.org/10.15407/emodel.39.01.075
2. Kantor, I.L. and Solodovnikov, A.S. (1973), Giperkompleksnye chisla [Hypercomplex numbers], Nauka, Ìoscow, USSR.
3. Kalinovsky, Ya.A. and Boyarinova, Yu.E. (2012), Vysokorazmernyie izomorfnyie giperkompleksnyie chislovyie sistemy i ikh ispolzovznie dlya povysheniya efektivnosti vychisleniy [High-dimensional isomorphic hypercomplex number systems and their use for increasing efficiency of calculations], Infodruk, Kyiv, Ukraine.
4. Kalinovsky, Ya.A., Lande, D.V., Boyarinova, Yu.E. and Khitsko, I.V. (2014), Some isomorphic classes for noncanonical hypercomplex number systems of dimension, arXiv preprint arXiv: 1403.2273, 2014.
5. Dieterich, E. (2005), Classification, automorphism groups and categorical structure of the twodimensional real division algebras, Journal of Algebra and its Applications, no. 4, pp. 517-538.
6. Sinkov, M.V., Kalinovsky, Ya.A. and Boyarinova, Yu.E. (2010), Konechnomernyie giperkompleksnyie chislovyie sistemy. Osnovy teorii. Primeneniya [Finite-dimensional hypercomplex number systems. Fundamentals of the theory. Applications], Infodruk, Kyiv, Ukraine.
7. E. Darpö, E. and Rochdi, A. (2011), “Classification of the four-dimensional power-commutative real division algebras”, Proceedings of the Royal Society of Edinburgh: Section A Mathema- tics, Vol. 141, Iss. 6, pp. 1207-1223.
https://doi.org/10.1017/S0308210510000259