On direct sums of cyclic groups with invariant monomorphisms
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 60-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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Direct sums of cyclic groups with left or right invariant monomorphisms are described.
Keywords: left or right invariant monomorphisms, endomorphism ring, direct sum of cyclic groups
Mots-clés : torsion complete group.
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A. R. Chekhlov. On direct sums of cyclic groups with invariant monomorphisms. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 60-65. http://geodesic.mathdoc.fr/item/VTGU_2013_3_a7/

[1] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial Press, M., 2007

[2] Chekhlov A. R., “Ob abelevykh gruppakh s normalnym koltsom endomorfizmov”, Algebra i logika, 48:4 (2009), 520–539 | MR | Zbl

[3] Grinshpon S. Ya., “Pochti gomomorfno izomorfnye abelevy gruppy”, Trudy Tomsk. un-ta, 220, 1975, 78–84

[4] Hausen J., Johnson J. A., “Abelian groups with many automorphisms”, Rend. Semin. Mat. Univ. Padova, 55 (1976 (1977)), 1–5 | MR

[5] Reid J. D., “On subcommutative rings”, Acta Math. Acad. Sci. Hungar., 16 (1965), 23–26 | DOI | MR | Zbl

[6] Lanver D. A., “Abelian groups in which endomorphic images are fully invariant”, J. Algebra, 29 (1974), 232–245 | DOI | MR

[7] Fomin A. A., “Abelevy gruppy so svobodnymi podgruppami beskonechnogo indeksa i ikh koltsa endomorfizmov”, Matem. zametki, 36:2 (1984), 179–187 | Zbl

[8] Kulikov L. Ya., “K teorii abelevykh grupp proizvolnoi moschnosti”, Matem. sb., 16:2 (1945), 129–162 | Zbl

[9] Krylov P. A., “Prodolzhenie izomorfizmov v abelevykh $p$-gruppakh”, Matem. zametki, 14:4 (1973), 543–548 | MR

[10] Tsarev A. V., “Nekotorye morfizmy modulei nad koltsom psevdoratsionalnykh chisel”, Sib. matem. zhurn., 49:4 (2008), 945–953 | MR | Zbl

[11] Sebeldin A. M., Chistyakov D. N., “Opredelyaemost abelevykh grupp tsentrom ikh koltsa endomorfizmov”, Matem. zametki, 84:6 (2008), 952–954 | DOI | MR | Zbl

[12] Blagoveschenskaya E. A., “Opredelyaemost abelevykh grupp bez krucheniya schetnogo ranga nekotorogo klassa ikh koltsami endomorfizmov”, Fund. i prikl. matem., 13:1 (2007), 31–43 | MR

[13] Mishina A. P., “Ob avtomorfizmakh i endomorfizmakh abelevykh grupp, II”, Vestn. Mosk. un-ta. Matem. i mekhan., 1972, no. 1, 62–66

[14] Abyzov A. N., Tuganbaev A. A., “Gomomorfizmy, blizkie k regulyarnym, i ikh prilozheniya”, Fund. i prikl. matem., 16:7 (2010), 3–38

[15] Chekhlov A. R., “Ob abelevykh cs-gruppakh bez krucheniya”, Izv. vuzov. Matematika, 1990, no. 3, 84–87 | MR | Zbl

[16] Chekhlov A. R., “Ob odnom klasse endotranzitivnykh grupp”, Matem. zametki, 69:6 (2001), 944–949 | DOI | MR | Zbl

[17] Chekhlov A. R., “Svoistva podgrupp abelevykh grupp, invariantnykh otnositelno proektsii”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2008, no. 1(2), 76–82

[18] Chekhlov A. R., “O proektivno invariantnykh podgruppakh abelevykh grupp”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2009, no. 1(5), 31–36

[19] Chekhlov A. R., “O nekotorykh klassakh nilgrupp”, Matem. zametki, 91:2 (2012), 297–304 | DOI | MR | Zbl

[20] Chekhlov A. R., “O proektivnom kommutante abelevykh grupp”, Sib. matem. zhurn., 53:2 (2012), 451–464 | MR | Zbl

[21] Chekhlov A. R., “Ob abelevykh gruppakh s nilpotentnymi kommutatorami endomorfizmov”, Izv. vuzov. Matematika, 2012, no. 10, 60–73 | Zbl

[22] Chekhlov A. R., “O proektivno razreshimykh abelevykh gruppakh”, Sib. matem. zhurn., 53:5 (2012), 1157–1165 | MR | Zbl

[23] Kozhukhov S. F., “Regulyarno polnye abelevy gruppy”, Izv. vuzov. Matematika, 1980, no. 12, 14–19 | MR | Zbl

[24] Danchev P. V., “Quasi-complete Q-groups are bounded”, Vladikavk. matem. zhurn., 10:1 (2008), 24–26 | MR

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

[26] Martynov L. M., “O primarnykh i redutsirovannykh mnogoobraziyakh monoassotsiativnykh algebr”, Sib. matem. zhurn., 42:1 (2001), 103–112 | MR | Zbl

[27] Tuganbaev A. A., “Avtomorfizmy podmodulei i ikh prodolzheniya”, Diskret. matem., 25:1 (2013), 144–151 | DOI | Zbl