Geodesic
Isomorphisms of semigroups of endomorphisms of mixed Abelian groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 54-60.

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

We study Abelian groups such that their endomorphism ring is a unique addition ring. It means that there exists a unique binary operation of addition which turns endomorphism semigroup into a ring. We solve also close questions.
Keywords: mixed Abelian group, endomorphism semigroup, $\mathrm{UA}$-ring. 
@article{IVM_2018_7_a3,
     author = {D. S. Chistyakov},
     title = {Isomorphisms of semigroups of endomorphisms of mixed {Abelian} groups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--60},
     publisher = {mathdoc},
     number = {7},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_7_a3/}
}
TY  - JOUR
AU  - D. S. Chistyakov
TI  - Isomorphisms of semigroups of endomorphisms of mixed Abelian groups
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 54
EP  - 60
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_7_a3/
LA  - ru
ID  - IVM_2018_7_a3
ER  - 
%0 Journal Article
%A D. S. Chistyakov
%T Isomorphisms of semigroups of endomorphisms of mixed Abelian groups
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 54-60
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_7_a3/
%G ru
%F IVM_2018_7_a3
D. S. Chistyakov. Isomorphisms of semigroups of endomorphisms of mixed Abelian groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2018), pp. 54-60. http://geodesic.mathdoc.fr/item/IVM_2018_7_a3/

[1] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial press, M., 2006

[2] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974

[3] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977

[4] Sebeldin A. M., “Abelevy gruppy s izomorfnymi polugruppami endomorfizmov”, UMN, 49:6 (1994), 211–212

[5] Sebeldin A. M., “Abelevy gruppy nekotorykh klassov s izomorfnymi koltsami endomorfizmov”, UMN, 50:1 (1995), 207–208

[6] Puusemp P., “Ob opredelyaemosti periodicheskoi abelevoi gruppy svoei polugruppoi endomorfizmov v klasse vsekh grupp”, Izv. AN Est. SSR, Fiz. matem., 29:3 (1980), 241–245 | Zbl

[7] Puusemp P., “Ob opredelyaemosti periodicheskoi abelevoi gruppy svoei polugruppoi endomorfizmov v klasse vsekh periodicheskikh abelevykh grupp”, Izv. AN Est. SSR, Fiz. matem., 29:3 (1980), 246–253 | Zbl

[8] May W., Toubassi E., “Endomorphisms of Abelian groups and the theorem of Baer and Kaplansky”, J. Algebra, 43:1 (1976), 1–13 | DOI | MR | Zbl

[9] Mikhalev A. V., “Multiplikativnaya klassifikatsiya assotsiativnykh kolets”, Matem. sb., 135:2 (1988), 210–214

[10] Stephenson W., “Unique addition rings”, Can. J. Math., 21:6 (1969), 210–214 | MR

[11] Lyubimtsev O. V., “Separabelnye abelevy gruppy bez krucheniya s $\mathrm{UA}$-koltsami endomorfizmov”, Fundament. i prikl. matem., 4:4 (1998), 1419–1422 | Zbl

[12] Lyubimtsev O. V., “Periodicheskie abelevy gruppy s $\mathrm{UA}$-koltsami endomorfizmov”, Matem. zametki, 70:5 (2001), 736–741 | DOI | Zbl

[13] Lyubimtsev O. V., Chistyakov D. S., “Ob abelevykh gruppakh bez krucheniya s $\mathrm{UA}$-koltsom endomorfizmov”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2011, no. 2 (14), 55–58

[14] Lyubimtsev O. V., Chistyakov D. S., “Smeshannye abelevy gruppy s izomorfnymi polugruppami endomorfizmov”, Matem. zametki, 97:4 (2015), 556–565 | DOI | MR | Zbl

[15] Lyubimtsev O. V., “Vpolne razlozhimye faktorno delimye abelevy gruppy s $\mathrm{UA}$-koltsami endomorfizmov”, Matem. zametki, 98:1 (2015), 125–133 | DOI

[16] Lyubimtsev O. V., Chistyakov D. S., “Moduli bez krucheniya s $\mathrm{UA}$-koltsami endomorfizmov”, Matem. zametki, 98:6 (2015), 898–906 | DOI | MR | Zbl

[17] Lyubimtsev O. V., “Algebraicheski kompaktnye abelevy gruppy s $\mathrm{UA}$-koltsami endomorfizmov”, Fundament. i prikl. matem., 20:5 (2015), 121–129

[18] Lyubimtsev O. V., Chistyakov D. S., “$\mathrm{UA}$-svoistva modulei nad kommutativnymi neterovymi koltsami”, Izv. vuzov. Matem., 2016, no. 11, 42–52 | MR | Zbl

[19] Breaz S., “On a class of mixed groups with semilocal Walk-endomorphism ring”, Comm. Algebra, 30:9 (2002), 4473–4485 | DOI | MR | Zbl

[20] Albrecht U., Goeters P., Wickless W., “The flat dimension of mixed Abelian groups as E-modules”, Rocky Mount. J., 25:2 (1995), 569–590 | DOI | MR | Zbl