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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 500, Pages 16–22
DOI: https://doi.org/10.31857/S2686954321050192 (Mi danma197) 		 
MATHEMATICS

Axiomatic definition of small cancellation rings

A. S. Atkarskayaab, A. Ya. Kanel-Belovacd, E. B. Plotkina, E. Ripsb

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
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DOI: https://doi.org/10.31857/S2686954321050192
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.
Funding agency Grant number
Israel Science Foundation 1994/20
Russian Science Foundation 17-11-01377
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.
Presented: A. L. Semenov
Received: 18.01.2021
Revised: 15.03.2021
Accepted: 18.08.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 2, Pages 234–239
DOI: https://doi.org/10.1134/S1064562421050197
Bibliographic databases:
Document Type: Article
UDC: 512.555, 512.543
Language: Russian
Citation: A. S. Atkarskaya, A. Ya. Kanel-Belov, E. B. Plotkin, E. Rips, “Axiomatic definition of small cancellation rings”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 16–22; Dokl. Math., 104:2 (2021), 234–239
Citation in format AMSBIB
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\paper Axiomatic definition of small cancellation rings
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2021
\vol 500
\pages 16--22
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\crossref{https://doi.org/10.31857/S2686954321050192}
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\transl
\jour Dokl. Math.
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\pages 234--239
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