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 | |
| State | Published - Sep 2021 |
Bibliographical note
Publisher Copyright:© 2021, Pleiades Publishing, Ltd.
Funding
The research of the first and third authors was supported by ISF (grant 1994/20) and the Emmy Noether Research Institute for Mathematics. The research of the first and fourth authors was also supported by the ISF fellowship. The research of the second author was supported by the Russian Science Foundation, grant 17-11-01377.
| Funders | Funder number |
|---|---|
| Emmy Noether Research Institute for Mathematics | |
| Israel Science Foundation | 1994/20 |
| Russian Science Foundation | 17-11-01377 |
Keywords
- defining relations in rings
- group algebra
- multi-turn
- small cancellation group
- small cancellation ring
- turn