A. S. Atkarskaya, A. Ya. Kanel-Belov, E. B. Plotkin, E. Rips, “Axiomatic definition of small cancellation rings”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 500,Pages <nobr>16

This article is cited in 1 paper

MATHEMATICS

Axiomatic definition of small cancellation rings

A. S. Atkarskaya^ab, A. Ya. Kanel-Belov^acd, E. B. Plotkin^a, E. Rips^b

^a Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel
^b Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
^c Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia
^d College of Mathematics and Statistics, Shenzhen University, Shenzhen, China

Abstract: In the present paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three specific axioms for corresponding defining relations that provide the small cancellation properties of the obtained ring. We show that this ring is nontrivial. It is called a small cancellation ring.

Keywords: small cancellation ring, turn, multi-turn, defining relations in rings, small cancellation group, group algebra.

UDC: 512.555, 512.543

Presented: A. L. Semenov
Received: 18.01.2021
Revised: 15.03.2021
Accepted: 18.08.2021

DOI: 10.31857/S2686954321050192