Varieties of Exponential R-Groups

M. G. Amaglobeli, A. G. Myasnikov, T. T. Nadiradze

Research output: Contribution to journalArticlepeer-review

Abstract

The notion of an exponential R-group, where R is an arbitrary associative ring with unity, was introduced by R. Lyndon. Myasnikov and Remeslennikov refined the notion of an R-group by introducing an additional axiom. In particular, the new concept of an exponential MR-group (R-ring) is a direct generalization of the concept of an R-module to the case of noncommutative groups. We come up with the notions of a variety of MR-groups and of tensor completions of groups in varieties. Abelian varieties of MR-groups are described, and various definitions of nilpotency in this category are compared. It turns out that the completion of a 2-step nilpotent MR-group is 2-step nilpotent.

Original languageEnglish
Pages (from-to)119-136
Number of pages18
JournalAlgebra and Logic
Volume62
Issue number2
DOIs
StatePublished - May 2023

Keywords

  • Lyndon’s R-group
  • MR-group
  • R-commutant
  • nilpotent MR-group
  • tensor completion
  • variety of MR-groups
  • α-commutator

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