Semifields with generator
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 25-33

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

The article deals with the theory of semirings and semifields. The definition of semifield's generator is given. It is shown that any semifield is embedded into a semifield with generator. Spectral characteristics of semifield with generator are also given.
Keywords: semifield, kernel of semifield, semifield's generator, irreducible spectrum.
E. M. Vechtomov; A. V. Cheraneva. Semifields with generator. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2009), pp. 25-33. http://geodesic.mathdoc.fr/item/VUU_2009_3_a2/
@article{VUU_2009_3_a2,
     author = {E. M. Vechtomov and A. V. Cheraneva},
     title = {Semifields with generator},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {25--33},
     year = {2009},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_3_a2/}
}
TY  - JOUR
AU  - E. M. Vechtomov
AU  - A. V. Cheraneva
TI  - Semifields with generator
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2009
SP  - 25
EP  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2009_3_a2/
LA  - ru
ID  - VUU_2009_3_a2
ER  - 
%0 Journal Article
%A E. M. Vechtomov
%A A. V. Cheraneva
%T Semifields with generator
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2009
%P 25-33
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2009_3_a2/
%G ru
%F VUU_2009_3_a2

[1] Weinert H. J., “Ein Struktursatz fur idempotente Halbkorper”, Acta Math. Acad. Sci. Hung, 15:3–4 (1964), 289–295 | DOI | MR | Zbl

[2] Polin S. V., “Prostye polutela i polupolya”, Sibirskii matematicheskii zhurnal, 15:1 (1974), 90–101 | MR | Zbl

[3] Hutchins H. C., Weinert H. J., “Homomorphisms and kernel of semifields”, Periodica Mathematica, 21:2 (1990), 113–152 | DOI | MR | Zbl

[4] Varankina V. I., Vechtomov E. M., Semenova I. A., “Polukoltsa nepreryvnykh neotritsatelnykh funktsii: delimost, idealy, kongruentsii”, Fundamentalnaya i prikladnaya matematika, 4:2 (1998), 493–510 | MR | Zbl

[5] Vechtomov E. M., “O svoistvakh polutel”, Matematicheskii vestnik pedvuzov i universitetov Volgo-Vyatskogo regiona, 2001, no. 3, 11–20

[6] Semenov A. N., “O reshetke kongruentsii polutel”, Vestnik VyatGGU, 2003, no. 9, 92–95

[7] Cheraneva A. V., “O kongruentsiyakh na polutelakh”, Chebyshevskii sbornik, 6:4(16) (2005), 164–171 | MR | Zbl

[8] Vechtomov E. M., Cheraneva A. V., “K teorii polutel”, Uspekhi matematicheskikh nauk, 63:2 (2008), 161–162 | DOI | MR | Zbl

[9] Golan J. S., Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999 | MR

[10] Birkgof G., Teoriya reshetok, Nauka, M., 1984 | MR

[11] Kopytov V. M., Reshetochno uporyadochennye gruppy, Nauka, M., 1984 | MR | Zbl

[12] Chuprakov D. V., “O glavnykh yadrakh polupolei nepreryvnykh funktsii”, Sovremennaya matematika i matematicheskoe obrazovanie, problemy istorii i filosofii matematiki, Mezhdunarodnaya nauchnaya konferentsiya, Tambov, 2008, 33–36