On a generalization of the concept of polyadic numbers
Čebyševskij sbornik, Tome 10 (2009) no. 2, pp. 109-122.

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

In this article we investigate several constructions of a polyadic numbers that allow to construct some generalization — a ring of halfpolyadic numbers, for which we extend a classic results: build a measure theory, a theory of integration, which is tightly bounded with probability properties of integers and real numbers.
@article{CHEB_2009_10_2_a4,
     author = {I. Y. Sukharev},
     title = {On a generalization of the concept of polyadic numbers},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {109--122},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a4/}
}
TY  - JOUR
AU  - I. Y. Sukharev
TI  - On a generalization of the concept of polyadic numbers
JO  - Čebyševskij sbornik
PY  - 2009
SP  - 109
EP  - 122
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a4/
LA  - ru
ID  - CHEB_2009_10_2_a4
ER  - 
%0 Journal Article
%A I. Y. Sukharev
%T On a generalization of the concept of polyadic numbers
%J Čebyševskij sbornik
%D 2009
%P 109-122
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a4/
%G ru
%F CHEB_2009_10_2_a4
I. Y. Sukharev. On a generalization of the concept of polyadic numbers. Čebyševskij sbornik, Tome 10 (2009) no. 2, pp. 109-122. http://geodesic.mathdoc.fr/item/CHEB_2009_10_2_a4/

[1] Hensel K., Theorie der algebraischen Zahlen, Teubner, Leipzig, 1908 | Zbl

[2] Mahler K., Introduction to $p$-adic numbers and their functions, Cambridge University press, 1973 | MR

[3] Prüfer H., “Neue Begründung der algebraischen Zahlentheorie”, Math. Ann., 94:1 (1925), 198–243 | MR

[4] Neumann J. von, “Zur Prüferschen Theorie der idealen Zahlen”, Acta Litt. Sci. Szeged, 2 (1926), 193–227 | Zbl

[5] Van Dantzig M. D., “Nombres universels $\nu!$-adiques avec une introduction sur l'algèbre topologique”, Ann. Sci. de l'École Norm. Sup., 53 (1936), 275–307

[6] Novoselov E. V., Vvedenie v poliadicheskii analiz, Uchebnoe posobie po spetskursu, Petrozavodsk, 1982 | MR

[7] Novoselov E. V., “Ob integrirovanii na odnom bikompaktnom koltse i ego prilozheniyakh k teorii chisel”, Izv. vysshikh ucheb. zavedenii. Matematika, 1961, no. 3 (22), 66–79 | MR | Zbl

[8] Novoselov E. V., “O nekotorykh topologicheskikh svoistvakh naturalnykh chisel”, Izv. vysshikh ucheb. zavedenii. Matematika, 1961, no. 1 (20), 119–129 | MR | Zbl

[9] Postnikov A. G., Vvedenie v analiticheskuyu teoriyu chisel, Nauka, M., 1971 | MR

[10] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972 | MR