Geodesic
Laterally complete $C_\infty(Q)$-modules
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 69-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $X$ be a regular laterally complete $C_\infty(Q)$-module and $\mathscr B$ be a Boolean algebra whose Stone space is $Q$. We introduce the passport $\Gamma(X)$ for $X$ consisting of uniquely defined partition of unity in $\mathscr B$ and set of pairwise different cardinal numbers. It is proved that $C_\infty(Q)$-modules $X$ and $Y$ are isomorphic if and only if $\Gamma(X)=\Gamma(Y)$. 
@article{VMJ_2014_16_2_a7,
     author = {V. I. Chilin and J. A. Karimov},
     title = {Laterally complete $C_\infty(Q)$-modules},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {69--78},
     year = {2014},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a7/}
}
TY  - JOUR
AU  - V. I. Chilin
AU  - J. A. Karimov
TI  - Laterally complete $C_\infty(Q)$-modules
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 69
EP  - 78
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a7/
LA  - ru
ID  - VMJ_2014_16_2_a7
ER  - 
%0 Journal Article
%A V. I. Chilin
%A J. A. Karimov
%T Laterally complete $C_\infty(Q)$-modules
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 69-78
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a7/
%G ru
%F VMJ_2014_16_2_a7
V. I. Chilin; J. A. Karimov. Laterally complete $C_\infty(Q)$-modules. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 69-78. http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a7/

[1] Aleksandrov P. S., Vvedenie v teoriyu mnozhestv i obschuyu topologiyu, Nauka, M., 1977, 368 pp. | MR

[2] Vladimirov D. A., Bulevy algebry, Nauka, M., 1969, 319 pp. | MR

[3] Karimov Zh. A., “Moduli Kaplanskogo–Gilberta nad algebroi izmerimykh funktsii”, Uzb. mat. zhurn., 2010, no. 4, 74—81 | MR

[4] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1975, 432 pp. | MR

[5] Kusraev A. G., Vektornaya dvoistvennost i ee prilozheniya, Nauka, Novosibirsk, 1985, 256 pp. | MR

[6] Kusraev A. G., Mazhoriruemye operatory, Nauka, M., 2003, 620 pp. | MR

[7] Muratov M. A., Chilin V. I., Algebry izmerimykh i lokalno izmerimykh operatorov, Tr. in-ta matematiki NAN Ukrainy, 69, 2007, 307 pp.

[8] Chilin V. I., “Chastichno uporyadochennye berovskie involyutivnye algebry”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie napravleniya, 27, VINITI, M., 1985, 99–128 | MR | Zbl

[9] Kaplansky J., “Projections in Banach algebras”, Ann. Math., 53 (1951), 235–249 | DOI | MR | Zbl

[10] Kaplansky J., “Algebras of type I”, Ann. Math., 56 (1952), 450–472 | DOI | MR

[11] Kaplansky J., “Modules over operator algebras”, Amer. J. Math., 75:4 (1953), 839–858 | DOI | MR | Zbl