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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 2, Pages 12–18 (Mi vmj576)  

Category of $\mathrm{MR}$-groups over a ring $\mathrm R$

M. G. Amaglobeli

Tbilisi Ivane Javakhishvili State University, Tbilisi, Georgia

Abstract: The category of exponential $\mathrm{MR}$-groups for an associative ring $\mathrm R$ with unity is defined in [1]. The present paper is devoted to the study of partial exponential $\mathrm{MR}$-groups which are isomorphically embedded in their tensor completion over the ring $\mathrm R$. The key to its understanding is the notion of tensor completion introduced in [1]. As a consequence, the description of free $\mathrm{MR}$-groups in the language of group constructions is obtained.

Key words: exponential $\mathrm R$-group, Lyndon $\mathrm R$-group, Hall $\mathrm R$-group, $\mathrm{MR}$-group, partial $\mathrm{MR}$-group, tensor completion.

Full text: PDF file (219 kB)
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UDC: 519.45
Received: 29.10.2015

Citation: M. G. Amaglobeli, “Category of $\mathrm{MR}$-groups over a ring $\mathrm R$”, Vladikavkaz. Mat. Zh., 18:2 (2016), 12–18

Citation in format AMSBIB
\Bibitem{Ama16}
\by M.~G.~Amaglobeli
\paper Category of $\mathrm{MR}$-groups over a~ring~$\mathrm R$
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 2
\pages 12--18
\mathnet{http://mi.mathnet.ru/vmj576}


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