Axiomatic Definition of Small Cancellation Rings

A. Atkarskaya; A. Kanel-Belov; E. Plotkin; E. Rips

doi:10.1134/s1064562421050197

Axiomatic Definition of Small Cancellation Rings

A. Atkarskaya^*, A. Kanel-Belov^*, E. Plotkin^*, E. Rips^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	234-239
Number of pages	6
Journal	Doklady Mathematics
Volume	104
Issue number	2
DOIs	https://doi.org/10.1134/s1064562421050197
State	Published - Sep 2021

Bibliographical note

Publisher Copyright:
© 2021, Pleiades Publishing, Ltd.

Keywords

defining relations in rings
group algebra
multi-turn
small cancellation group
small cancellation ring
turn

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Axiomatic Definition of Small Cancellation Rings

Abstract

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Keywords

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