Category of MRR-Groups over a Ring RR

		ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online)

Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Contacts Address: Markusa st. 22, Vladikavkaz, 362027, RNO-A, Russia Phone: (8672)50-18-06 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.5914 Category of MRR-Groups over a Ring RR Amaglobeli M. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2. Abstract: The category of exponential MRR-groups for an associative ring RR with unity is defined in [1]. The present paper is devoted to the study of partial exponential MRR-groups which are isomorphically embedded in their tensor completion over the ring RR. The key to its understanding is the notion of tensor completion introduced in [1]. As a consequence, the description of free MRR-groups in the language of group constructions is obtained. Keywords: exponential RR-group, Lyndon RR-group, Hall RR-group, MRR-group, partial MRR-group, tensor completion. Language: Russian Download the full text For citation: Amaglobeli M. Category of MRR-Groups over a ring RR // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 2, pp. 12-18. DOI 10.23671/VNC.2016.2.5914 + References Myasnikov A. G., Remeslennikov V. N. Groups with Exponents I. Fundamentals of the Theory and Tensor Completions. Sibirskij matematicheskij zhurnal [Siberian Math. J.], 1994, vol.35, no.5, pp.1106-1118 [in Russian]. Amaglobeli M. G., Remeslennikov V. N. Free Nilpotent \(R\)-groups of Class 2. Doklady Akademii Nauk, 2012, vol. 443, no. 4, pp. 410-413 [in Russian]. Amaglobeli M. G., Remeslennikov V. N. Extension of a centralizer in nilpotent groups. Sibirskij matematicheskij zhurnal [Siberian Math. J.], 2013, vol. 54, no. 1, pp. 8-19 [in Russian]. Polin S. V. Free decompositions in varieties of \(\lambda\)-groups. Matematicheskij sbornik [Mathematics Collection], 1972, vol. 87(129), no. 3, pp. 377-395 [in Russian]. ← Contents of issue


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