Geodesic
Endomorphism rings of rigid almost completely decomposable Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 31-47 
E. A. Blagoveshchenskaya. Endomorphism rings of rigid almost completely decomposable Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 7, pp. 31-47. http://geodesic.mathdoc.fr/item/FPM_2012_17_7_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A necessary and sufficient condition is found for rigid almost completely decomposable Abelian groups with $p$-primary regulator quotients to have endomorphism rings isomorphic to those of the corresponding groups with cyclic regulator quotients.

[1] Blagoveschenskaya E., Pochti vpolne razlozhimye gruppy i ikh koltsa endomorfizmov, Matematika v politekhnicheskom universitete, SPb., 2009

[2] Krylov P. A., Mikhalëv A. V., Tuganbaev A. A., Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial, M., 2006

[3] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974; т. 2, 1977

[4] Arnold D., Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., 931, Springer, 1982 | MR | Zbl

[5] Blagoveshchenskaya E., “Direct decompositions of almost completely decomposable Abelian groups”, Abelian Groups and Modules, Lect. Notes Pure Appl. Math., 182, Marcel Dekker, New York, 1996, 163–179 | MR | Zbl

[6] Blagoveshchenskaya E., Ivanov G., Schultz P., “The Baer–Kaplansky theorem for almost completely decomposable groups”, Contemp. Math., 273 (2001), 85–93 | DOI | MR | Zbl

[7] Blagoveshchenskaya E., Mader A., “Decompositions of almost completely decomposable Abelian groups”, Contemp. Math., 171 (1994), 21–36 | DOI | MR | Zbl

[8] Faticoni T., Schultz P., “Direct decompositions of ACD groups with primary regulating index”, Abelian Groups and Modules, Lect. Notes Pure Appl. Math., 182, Marcel Dekker, New York, 1996, 233–241 | MR | Zbl

[9] Mader A., Almost Completely Decomposable Abelian Groups, Algebra, Logic and Applications, 13, Gordon and Breach, Amsterdam, 1999

[10] Mader A., Almost Completely Decomposable Abelian Groups, Photocopied notes, Montreal, 1992

[11] Mader A., Schultz P., “Endomorphism rings and automorphism groups of almost completely decomposable groups”, Commun. Algebra, 28 (2000), 51–68 | DOI | MR | Zbl

[12] Mader A., Vinsonhaler C., “Classifying almost completely decomposable groups”, J. Algebra, 170:3 (1998), 754–780 | DOI | MR