On torsionfree~LCA groups with commutative rings of continuous endomorphisms
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 81-100.

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Let $\mathcal L$ be the class of locally compact abelian (LCA) groups. For certain subclasses $\mathcal S$ of $\mathcal L$, we obtain information about the groups $X\in\mathcal S$ such that the ring $E(X)$ of continuous endomorphisms of $X$ is commutative. The main results concern torsionfree groups, groups with splitting torsion subgroups and their duals.
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Valeriu Popa. On torsionfree~LCA groups with commutative rings of continuous endomorphisms. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 81-100. http://geodesic.mathdoc.fr/item/BASM_2007_2_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 3–8, Nauka, Moscow, 1969 | Zbl

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

[4] Charin V. S., “On groups of finite rank, II”, Ukr. Math. J., 18:3 (1966), 85–96 | DOI | MR | Zbl

[5] Griffith Ph., “Purely indecomposable torsionfree groups”, Proc. Amer. Math. Soc., 18:4 (1967), 738–742 | DOI | 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 rings of direct sums of groups”, Acta Scient. Math., 28:1–2 (1967), 21–29 | MR | Zbl

[8] Van Leeuwen L. C. A., “Remarks on endomorphism rings of torsion-free abelian groups”, Acta Scient. Math., 32:3–4 (1971), 345–350 | MR | Zbl

[9] Loth P., “The duals of almost completely decomposable groups”, Arch. Math., 68:5 (1997), 353–358 | DOI | MR | Zbl

[10] Mader A., Schultz Ph., “Endomorphism rings and automorphism groups of almost completely decomposable groups”, Comm. in Algebra, 28(1) (2000), 51–68 | DOI | MR | Zbl

[11] Moskalenko Z., “Locally compact abelian groups of finite rank”, Ukr. Math. J., 22:2 (1970), 174–181 | DOI | MR | Zbl

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

[13] Popa V., “On endomorphism rings without nonzero nilpotent elements, II”, Bul. Acad. Şti. R. Moldova, Matematica, 1999, no. 2(30), 91–104 | MR | Zbl

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

[15] Popa V., “On LCA groups in which some closed subgroups have commutative rings of continuous endomorphisms”, Bul. Acad. Şti. R. Moldova, Matematica, 2007, no. 1(53), 83–94 | MR | Zbl

[16] Schultz Ph., “On a paper of Szele and Szendrei on groups with commutative endomorphism rings”, Acta Math. Acad. Sci. Hung., 24:1–2 (1973), 59–63 | DOI | MR | Zbl

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

[18] Zelmanowitz J., “Commutative endomorphism rings”, Can. J. Math., XXIII:1 (1971), 69–76 | MR