Geodesic
On LCA groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 88-111.

Voir la notice de l'article provenant de la source Math-Net.Ru

We determine the structure of LCA (locally compact abelian) groups $X$ with the property that the ring $E(X)$ of continuous endomorphisms of $X$, taken with the compact-open topology, satisfies $DCC$ (descending chain condition) on different types of closed ideals. 
@article{BASM_2017_2_a7,
     author = {Valeriu Popa},
     title = {On {LCA} groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {88--111},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2017_2_a7/}
}
TY  - JOUR
AU  - Valeriu Popa
TI  - On LCA groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2017
SP  - 88
EP  - 111
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2017_2_a7/
LA  - en
ID  - BASM_2017_2_a7
ER  - 
%0 Journal Article
%A Valeriu Popa
%T On LCA groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2017
%P 88-111
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2017_2_a7/
%G en
%F BASM_2017_2_a7
Valeriu Popa. On LCA groups whose ring of continuous endomorphisms satisfies $DCC$ on closed ideals. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 88-111. http://geodesic.mathdoc.fr/item/BASM_2017_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] Armacost D. L., Armacost W. L., “On $\mathbb Q$-dense and densely divisible LCA groups”, Proc. Amer. Math. Sos., 36 (1976), 301–305 | MR

[3] Bourbaki N., Topologie generale, Chapter 1–2, Éléments de mathematique, Nauka, Moscow, 1968 | MR

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

[5] Bourbaki N., Topologie generale, Chapter 9–20, Éléments de mathematique, Nauka, Moscow, 1975 | Zbl

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

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

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

[9] Kertész A., Lectures on artinian rings, Académiai Kiadó, Budapest, 1987 | MR

[10] Lam T. Y., A first course in noncommutative rings, Graduate texts in mathematics, 131, Springer-Verlag, Berlin–Heidelberg–New York, 1991 | DOI | MR | Zbl

[11] Popa V., “Units, idempotents and nilpotents of an endomorphism ring. I”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 1996, no. 3(22), 83–93 | MR | Zbl

[12] Popa V., “On LCA groups whose rings of continuous endomorphisms have at most two non-trivial closed ideals. I”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2011, no. 3(67), 91–107 | MR | Zbl

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

[14] Rose H., Linear algebra: a pure mathematical approach, Birkhäuser Verlag, Basel–Boston–Berlin, 2002 | MR | Zbl

[15] Szász F., “Die abelschen Gruppen, deren volle Endomorphismenringe die Minimalbedingung für Hauptrechtsideale erfüllen”, Monatshefte Math., 65 (1961), 150–153 | DOI | MR | Zbl