On LCA groups with locally compact rings of continuous endomorphisms. I
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 65-79 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We determine the discrete abelian groups and the compact abelian groups with the property that their rings of continuous endomorphisms are locally compact in the compact-open topology.
@article{BASM_2014_3_a6,
     author = {Valeriu Popa},
     title = {On {LCA} groups with locally compact rings of continuous {endomorphisms.~I}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {65--79},
     year = {2014},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2014_3_a6/}
}
TY  - JOUR
AU  - Valeriu Popa
TI  - On LCA groups with locally compact rings of continuous endomorphisms. I
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2014
SP  - 65
EP  - 79
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/BASM_2014_3_a6/
LA  - en
ID  - BASM_2014_3_a6
ER  - 
%0 Journal Article
%A Valeriu Popa
%T On LCA groups with locally compact rings of continuous endomorphisms. I
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2014
%P 65-79
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2014_3_a6/
%G en
%F BASM_2014_3_a6
Valeriu Popa. On LCA groups with locally compact rings of continuous endomorphisms. I. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 65-79. http://geodesic.mathdoc.fr/item/BASM_2014_3_a6/

[1] Armacost D. L., The structure of locally compact abelian groups, Pure and Applied Mathematics Series, 68, Marcel Dekker, New York, 1981 | MR | Zbl

[2] Bourbaki N., Topologie generale, Chapter IX–X. Éléments de mathematique, Nauka, Moscow, 1975 | Zbl

[3] Braconnier J., “Sur les groupes topologiques localement compact”, J. Math. Pures Apl., 27:9 (1948), 1–85 | MR | Zbl

[4] Dikranjan D., Prodanov I., Stoyanov L., Topological groups, Pure and Applied Mathematics Series, 130, Marcel Dekker, New York–Basel, 1990 | MR | Zbl

[5] Fuchs L., Infinite abelian groups, v. 1, Academic Press, New York–London, 1970 | MR | Zbl

[6] Fuchs L., Infinite abelian groups, v. 2, Academic Press, New York–London, 1973 | MR | Zbl

[7] Hewitt E., Ross K., Abstract Harmonic Analysis, v. 1, Academic Press, New York, 1963

[8] Hungerford Th. W., Algebra, Springer-Verlag, New York, 1974 | MR

[9] Levin M., “The automorphism group of a locally compact abelian group”, Acta Math., 127 (1971), 259–278 | DOI | MR | Zbl

[10] Mel'nikov O., “Compactness conditions for groups of automorphisms of topological groups”, Mat. Zametki, 19:5 (1976), 735–743 | MR | Zbl

[11] Moskowitz M., “Homological algebra in locally compact abelian groups”, Trans. Amer. Math. Soc., 127 (1967), 361–404 | DOI | MR | Zbl

[12] Plaumann P., “Automorphism groups of locally compact abelian groups”, Lecture Notes Math., 874, 1981, 272–282 | DOI | MR | Zbl

[13] Robertson L., “Connectivity, divisibility, and torsion”, Trans. Amer. Math. Soc., 128 (1967), 482–505 | DOI | MR | Zbl