3 papers
math.RA2020
Small cancelation rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define…
math.RA2020
Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
Alexei Kanel-Belov, Alexei Chilikov, Ilya Ivanov-Pogodaev +4
This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and…
math.RA2018
Construction of a quotient ring of in which a binomial is invertible using small cancellation methods
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring , where $\mathbb{Z}_2\mathc…