Axiomatic Definition of Small Cancellation Rings

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 proper...

Full description

Saved in:
Bibliographic Details
Published in:Doklady. Mathematics 2021-09, Vol.104 (2), p.234-239
Main Authors: Atkarskaya, A., Kanel-Belov, A., Plotkin, E., Rips, E.
Format: Article
Language:English
Subjects:
Axioms
Cancellation
Group theory
Mathematics
Mathematics and Statistics
Quotients
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562421050197