Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 179, Pages 10–15
DOI: https://doi.org/10.36535/0233-6723-2020-179-10-15 (Mi into620) 		 
Spaces over algebras with Euclidean metric

N. I. Gusevaab

a Moscow State Pedagogical University
b Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.36535/0233-6723-2020-179-10-15
Abstract: In this paper, we propose a new approach to the real realization of spaces over algebras, in which a space over an algebra and the space of its realizations have the same dimension. We also give several examples from Euclidean geometry, which illustrate this real realization of spaces over linear algebras.
Keywords: space over algebra, structure of an algebra in a linear space, complex linear space, dimension, metric, real realization of a space.
Document Type: Article
UDC: 514.169
MSC: 13K05, 51N20, 51M04
Language: Russian
Citation: N. I. Guseva, “Spaces over algebras with Euclidean metric”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 179, VINITI, Moscow, 2020, 10–15
Citation in format AMSBIB
\Bibitem{Gus20}
\by N.~I.~Guseva
\paper Spaces over algebras with Euclidean metric
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 179
\pages 10--15
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into620}
\crossref{https://doi.org/10.36535/0233-6723-2020-179-10-15}
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