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Fundamentalnaya i Prikladnaya Matematika, 2007, Volume 13, Issue 1, Pages 229–233
(Mi fpm14)
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This article is cited in 6 scientific papers (total in 6 papers)
Abelian groups as endomorphic modules over their endomorphism ring
D. S. Chistyakova, O. V. Ljubimtsevb a Nizhny Novgorod State Pedagogical University
b Nizhny Novgorod State University of Architecture and Civil Engineering
Abstract:
Let $R$ be an associative ring with a unit and $N$ be a left $R$-module. The set
$M_R(N)=\{f\colon N\to N\mid f(rx)=rf(x),\ r\in R,\ x\in N\}$
is a near-ring with respect to the operations of addition and composition and contains the ring
$E_R(N)$ of all endomorphisms of the $R$-module $N$. The $R$-module $N$ is endomorphic if $M_R(N)=E_R(N)$. We call an Abelian group endomorphic if it is an endomorphic module over its endomorphism ring. In this paper, we find endomorphic Abelian groups in the classes of all separable torsion-free groups, torsion groups, almost completely decomposable torsion-free groups, and indecomposable torsion-free groups of rank 2.
Citation:
D. S. Chistyakov, O. V. Ljubimtsev, “Abelian groups as endomorphic modules over their endomorphism ring”, Fundam. Prikl. Mat., 13:1 (2007), 229–233; J. Math. Sci., 152:4 (2008), 604–607
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https://www.mathnet.ru/eng/fpm14 https://www.mathnet.ru/eng/fpm/v13/i1/p229
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Abstract page: | 379 | Full-text PDF : | 118 | References: | 47 | First page: | 1 |
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