Geodesic
On the completeness of topological rings in maximal topologies
Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 159-174 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article studies rings that are direct sums of an infinite family of subrings. The question of the completeness of these rings in maximal ring topologies is investigated for various classes of ring topologies. In particular it is shown that if the continuum hypothesis is assumed, then both complete and non-complete maximal ring topologies exist on a ring that is an infinite direct sum of copies of the same finite field. 
@article{SM_1996_187_2_a0,
     author = {V. I. Arnautov},
     title = {On the completeness of topological rings in maximal topologies},
     journal = {Sbornik. Mathematics},
     pages = {159--174},
     year = {1996},
     volume = {187},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/}
}
TY  - JOUR
AU  - V. I. Arnautov
TI  - On the completeness of topological rings in maximal topologies
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 159
EP  - 174
VL  - 187
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/
LA  - en
ID  - SM_1996_187_2_a0
ER  - 
%0 Journal Article
%A V. I. Arnautov
%T On the completeness of topological rings in maximal topologies
%J Sbornik. Mathematics
%D 1996
%P 159-174
%V 187
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/
%G en
%F SM_1996_187_2_a0
V. I. Arnautov. On the completeness of topological rings in maximal topologies. Sbornik. Mathematics, Tome 187 (1996) no. 2, pp. 159-174. http://geodesic.mathdoc.fr/item/SM_1996_187_2_a0/

[1] Graev M. I., “Svobodnye topologicheskie gruppy”, Izv. AN SSSR. Ser. matem., 12 (1948), 279–324 | MR | Zbl

[2] Tkachenko M. G., “O polnote svobodnykh abelevykh topologicheskikh grupp”, DAN SSSR, 269:2 (1983), 299–303 | MR

[3] Marco G. De, Orsatti, “Complete linear topologies on abelian groups”, Symp. Math. Jst naz alta mat. conv. nov-dic., 13 (1972), 153–161 | MR

[4] Arnautov V. I., Kabanova E. I., “Ob usilenii gruppovoi topologii schetnoi gruppy do polnoi”, Sib. matem. zhurn., 31:1 (1990), 3–13 | MR

[5] Arnautov V. I., “Ob usilenii koltsevoi topologii schetnogo koltsa do polnoi”, IV simpozium po teorii kolets i modulei, Tezisy soobschenii, Lvov, 1990

[6] Marin E. I., “Usilenie gruppovoi topologii Abelevoi gruppy do polnoi”, Moduli, algebry i topologii: Mat. issled., 1988, no. 105, 93–104 | MR

[7] Arnautov V. I., Zelenyuk E. G., “K probleme polnoty maksimalnykh topologicheskikh grupp”, Ukr. matem. zhurn., 43:1 (1991), 21–27 | MR | Zbl

[8] Arnautov V. I., “O polnote kolets v maksimalnykh topologiyakh”, Mezhdunarodnaya konferentsiya po algebre, posvyaschennaya pamyati A. I. Maltseva, Tezisy dokladov po teorii kolets, algebr i modulei, Novosibirsk, 1989

[9] Arnautov V. I., Vodinchar M. I., Mikhalev A. V., Vvedenie v teoriyu topologicheskikh kolets i modulei, Shtiintsa, Kishinev, 1981 | MR | Zbl

[10] Andrunakievich V. A., Ryabukhin Yu. M., “O nekotorykh klassakh slabo bulevykh kolets”, DAN SSSR, 224:1 (1975), 11–14 | MR | Zbl

[11] Arnautov V. I., Vodinchar M. I., Glavatskii S. T., Mikhalev A. V., Konstruktsii topologicheskikh kolets, Shtiintsa, Kishinev, 1988 | MR