Geodesic
Spaces over algebras with Euclidean metric
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 10-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, metric, real realization of a space.
Mots-clés : dimension 
@article{INTO_2020_179_a1,
     author = {N. I. Guseva},
     title = {Spaces over algebras with {Euclidean} metric},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {10--15},
     publisher = {mathdoc},
     volume = {179},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_179_a1/}
}
TY  - JOUR
AU  - N. I. Guseva
TI  - Spaces over algebras with Euclidean metric
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 10
EP  - 15
VL  - 179
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_179_a1/
LA  - ru
ID  - INTO_2020_179_a1
ER  - 
%0 Journal Article
%A N. I. Guseva
%T Spaces over algebras with Euclidean metric
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 10-15
%V 179
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_179_a1/
%G ru
%F INTO_2020_179_a1
N. I. Guseva. Spaces over algebras with Euclidean metric. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 10-15. http://geodesic.mathdoc.fr/item/INTO_2020_179_a1/

[5] Bakhman F., Shmidt E., $n$-Ugolniki, Mir, M., 1973

[6] Burlakov M. P., Gamiltonovy algebry, Graf-Press, M., 2006

[7] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Prostranstva nad algebrami, KGU, Kazan, 1985 | MR

[8] Guseva N. I., Burlakov I. M., Burlakov M. P., Elementarnaya geometriya v prostranstvakh nad algebrami, Intellekt-Tsentr, M., 2017

[9] Rozenfeld B. A., Neevklidovy geometrii, GITTL, M., 1955 | MR