Geodesic
Remark on coding in algebras with strong filtration
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2019), pp. 15-21 
V. N. Latyshev. Remark on coding in algebras with strong filtration. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2019), pp. 15-21. http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a2/
@article{VMUMM_2019_1_a2,
     author = {V. N. Latyshev},
     title = {Remark on coding in algebras with strong filtration},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {15--21},
     year = {2019},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a2/}
}
TY  - JOUR
AU  - V. N. Latyshev
TI  - Remark on coding in algebras with strong filtration
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 15
EP  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a2/
LA  - ru
ID  - VMUMM_2019_1_a2
ER  - 
%0 Journal Article
%A V. N. Latyshev
%T Remark on coding in algebras with strong filtration
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 15-21
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a2/
%G ru
%F VMUMM_2019_1_a2

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

The way of communication coding using “multiplicative gammation” in algebras with a strong filtration is proposed. This class of algebras was introduced earlier by the author for needs of Gröbner–Shirshov bases theory in a wide context. It includes semigroup algebras of ordered semigroups and universal envelopping algebras of Lie algebras, in particular, the polynomial algebra and free associative algebra.

[1] Latyshev V. N., “Algebraicheskaya simplikatsiya i kriptograficheskie motivy”, Fund. i prikl. matem., 19:2 (2014), 109–124

[2] Dorichenko S. A., Yaschenko V. V., 25 etyudov o shifrakh, TEIS, M., 1994

[3] Birkgof G., Barti T. K., Sovremennaya prikladnaya algebra, Lan, SPb., 2005

[4] Hurley B., Hurley T., Group ring cryptography, 2011, arXiv: 1104.1724v1 [math.GR] | MR

[5] Latyshev V. N., “Obschaya versiya standartnogo bazisa v assotsiativnykh algebrakh i proizvodnye konstruktsii”, Fund. i prikl. matem., 15:3 (2009), 183–203

[6] Latyshev V. N., “Svobodnoe proizvedenie algebr, dopuskayuschikh standartnye bazisy idealov”, Vestn. Mosk. un-ta. Matem. Mekhan., 2011, no. 3, 19–23 | Zbl

[7] Bergman G., “Ordering coproducts of groups and semigroups”, J. Algebra, 133:2 (1990), 313–339 | DOI | MR | Zbl

[8] Becker T., Weispfenning V., Gröbner-bases, Springer-Verlag, N. Y.–Berlin–L.–P., 1991 | MR

[9] Dzhekobson N., Algebry Li, Mir, M., 1964 | MR

[10] Morozov V. V., “Klassifikatsiya nilpotentnykh algebr Li shestogo poryadka”, Izv. vuzov. Matem., 1958, no. 415, 161–171 | Zbl

[11] Bermudez J. M. A., Goze M., “Classification des algébres de Lie nilpotentes complexes de dimension 7”, Arch. Math., 52:2 (1989), 175–185 | DOI | MR | Zbl

[12] Goze M., Bermudez J. M. A., “On the varieties of nilpotent Lie algebras of dimension 7 and 8”, J. Pure and Appl. Algebra, 77:2 (1992), 131–140 | DOI | MR | Zbl