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 language | English |
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Pages (from-to) | 119-136 |
Number of pages | 18 |
Journal | Algebra and Logic |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - May 2023 |
Keywords
- Lyndon’s R-group
- MR-group
- R-commutant
- nilpotent MR-group
- tensor completion
- variety of MR-groups
- α-commutator