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Algebra i logika, 2018, Volume 57, Number 2, Pages 137–148
DOI: https://doi.org/10.17377/alglog.2018.57.201
(Mi al840)
 

This article is cited in 6 scientific papers (total in 6 papers)

The tensor completion functor in categories of exponential $MR$-groups

M. G. Amaglobeli

Javakhishvili Tbilisi State University, pr. Chavchavadze 1, Tbilisi, 0128 Georgia
Full-text PDF (168 kB) Citations (6)
References:
Abstract: The notion of an exponential $R$-group, where $R$ is an arbitrary associative ring with unity, was introduced by R. Lyndon. A. G. Myasnikov and V. N. Remeslennikov refined this notion by adding an extra axiom. In particular, the new notion of an exponential $MR$-group is an immediate generalization of the notion of an $R$-module to the case of noncommutative groups. Basic concepts in the theory of exponential $MR$-groups are presented, and we propose a particular method for constructing tensor completion – the key construction in the category of $MR$-groups. As a consequence, free $MR$-groups and free $MR$-products are described using the language of group constructions.
Keywords: Lyndon $R$-group, Hall $R$-group, $MR$-group, $\alpha$-commutator, tensor completion.
Received: 09.08.2017
Revised: 14.11.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 2, Pages 89–97
DOI: https://doi.org/10.1007/s10469-018-9482-9
Bibliographic databases:
Document Type: Article
UDC: 512.544.33
Language: Russian
Citation: M. G. Amaglobeli, “The tensor completion functor in categories of exponential $MR$-groups”, Algebra Logika, 57:2 (2018), 137–148; Algebra and Logic, 57:2 (2018), 89–97
Citation in format AMSBIB
\Bibitem{Ama18}
\by M.~G.~Amaglobeli
\paper The tensor completion functor in categories of exponential $MR$-groups
\jour Algebra Logika
\yr 2018
\vol 57
\issue 2
\pages 137--148
\mathnet{http://mi.mathnet.ru/al840}
\crossref{https://doi.org/10.17377/alglog.2018.57.201}
\transl
\jour Algebra and Logic
\yr 2018
\vol 57
\issue 2
\pages 89--97
\crossref{https://doi.org/10.1007/s10469-018-9482-9}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000440418100001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050258176}
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  • https://www.mathnet.ru/eng/al/v57/i2/p137
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:249
    Full-text PDF :38
    References:35
    First page:6
     
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