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Matematicheskie Zametki, 2013, Volume 94, Issue 4, Pages 620–627
DOI: https://doi.org/10.4213/mzm9378 (Mi mzm9378) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Torsion-Free Weakly Transitive $E$-Engel Abelian Groups

A. R. Chekhlov

Tomsk State University
Full-text PDF (430 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm9378
Abstract: It is proved that if all the endomorphisms of a reduced torsion-free weakly transitive Abelian group are bounded right-nilpotent, then its ring of endomorphisms is commutative. The ring of endomorphisms of a torsion-free Abelian group with periodic group of automorphisms and Engel ring of endomorphisms is also commutative.
Keywords: $E$-Engel Abelian group, weakly transitive group, torsion-free Abelian group, ring of endomorphisms, periodic group of automorphisms, $n$-step Engel ring, Lie algebra, $E$-nilpotent group, nilpotent element of a ring.
Received: 15.11.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 4, Pages 583–589
DOI: https://doi.org/10.1134/S0001434613090289
Bibliographic databases:
Document Type: Article
UDC: 512.541
Language: Russian
Citation: A. R. Chekhlov, “Torsion-Free Weakly Transitive $E$-Engel Abelian Groups”, Mat. Zametki, 94:4 (2013), 620–627; Math. Notes, 94:4 (2013), 583–589
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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