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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
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
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
Linking options:
https://www.mathnet.ru/eng/al840 https://www.mathnet.ru/eng/al/v57/i2/p137
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Abstract page: | 249 | Full-text PDF : | 38 | References: | 35 | First page: | 6 |
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