Geodesic
E-groups and E-rings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 159 (2019), pp. 111-132

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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, $E$-ring, $T$-ring, $A$-ring, endomorphism ring.
Mots-clés : $E$-group, quotient divisible group 
@article{INTO_2019_159_a3,
     author = {P. A. Krylov and A. A. Tuganbaev and A. V. Tsarev},
     title = {E-groups and {E-rings}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {111--132},
     publisher = {mathdoc},
     volume = {159},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_159_a3/}
}
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P. A. Krylov; A. A. Tuganbaev; A. V. Tsarev. E-groups and E-rings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 159 (2019), pp. 111-132. http://geodesic.mathdoc.fr/item/INTO_2019_159_a3/