Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 159, Pages 111–132 (Mi into417)  
This article is cited in 2 scientific papers (total in 2 papers)

E-groups and E-rings

P. A. Krylova, A. A. Tuganbaevbc, A. V. Tsarevd

a National Research Tomsk State University
b National Research University "Moscow Power Engineering Institute"
c Lomonosov Moscow State University
d Moscow State Pedagogical University
Full-text PDF (387 kB) Citations (2)
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Abstract: An associative ring $R$ is called an $E$-ring if the canonical homomorphism $R\cong \textsf{E}(R^+)$ is an isomorphism. Additive groups of $E$-rings are called $E$-groups. In other words, an Abelian group $A$ is an $E$-group if and only if $A\cong \operatorname{End} A$ and the endomorphism ring $\textsf{E}(A)$ is commutative. In this paper, we give a survey of the main results on $E$-groups and $E$-rings and also consider some of their generalizations: $\mathcal{E}$-closed groups, $T$-rings, $A$-rings, the groups admitting only commutative multiplications, etc.
Keywords: Abelian group, $\mathcal{E}$-closed group, $E$-group, $E$-ring, $T$-ring, quotient divisible group, $A$-ring, endomorphism ring.
Funding agency Grant number
Russian Science Foundation 16-11-10013
The work of A. A. Tuganbaev was supported by the Russian Science Foundation (project No. 16-11-10013).
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 256, Issue 4, Pages 341–361
DOI: https://doi.org/10.1007/s10958-021-05430-2
Bibliographic databases:
Document Type: Article
UDC: 512.541
MSC: 20Kxx
Language: Russian
Citation: P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “E-groups and E-rings”, Algebra, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 159, VINITI, Moscow, 2019, 111–132; J. Math. Sci. (N. Y.), 256:4 (2021), 341–361
Citation in format AMSBIB
\Bibitem{KryTugTsa19}
\by P.~A.~Krylov, A.~A.~Tuganbaev, A.~V.~Tsarev
\paper E-groups and E-rings
\inbook Algebra
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 159
\pages 111--132
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into417}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3939219}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 256
\issue 4
\pages 341--361
\crossref{https://doi.org/10.1007/s10958-021-05430-2}
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