Geodesic
On LCA groups in which some closed subgroups have commutative rings of continuous endomorphisms
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 83-94
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We describe here the locally compact abelian (LCA) groups all of whose closed polythetic, respectively, copolythetic subgroups have commutative rings of continuous endomorphisms. We also determine the LCA groups all of whose polythetic, respectively, copolythetic quotients by closed subgroups have commutative rings of continuous endomorphisms. 
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}
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Valeriu Popa. On LCA groups in which some closed subgroups have commutative rings of continuous endomorphisms. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 83-94. http://geodesic.mathdoc.fr/item/BASM_2007_1_a7/

[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. Éléments de mathematique, Chapter 1–2, Nauka, Moscow, 1968 | Zbl

[3] Bourbaki N., Topologie generale.Éléments de mathematique, Chapter 3–8, Nauka, Moscow, 1969 | Zbl

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

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

[6] Hewitt E., Ross K., Abstract Harmonic Analysis, Vol. 1, Nauka, Moscow, 1975 | MR

[7] Van Leeuwen L. C. A., “On the endomorphism ring of direct sums of groups”, Acta Scient. Math., 28:1–2 (1967), 21–29 | MR | Zbl

[8] Morris S. A., Pontryagin duality and the structure of locally compact abelian groups, Cambridge University Press, Cambridge, 1977 | MR | Zbl

[9] Orsatti A., Introduzione ai gruppi abeliani astratti e topologici, Quaderni dell'Unione Matematica Italiana, 8, Pitagora Editrice, Bologna, 1979 | Zbl

[10] Popa V., “On topological torsion LCA groups with commutative ring of continuous endomorphisms”, Bul. Acad. Şt. Rep.. Moldova, Matematica, 2006, no. 3(52), 87–100 | MR | Zbl

[11] Szele T., Szendrei J., “On abelian groups with commutative endomorphism ring”, Acta Math. Acad. Sci. Hung., 2 (1951), 309–324 | DOI | MR | Zbl