Geodesic
Axiomatic definition of small cancellation rings
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 16-22

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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. 
@article{DANMA_2021_500_a2,
     author = {A. S. Atkarskaya and A. Ya. Kanel-Belov and E. B. Plotkin and E. Rips},
     title = {Axiomatic definition of small cancellation rings},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {16--22},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a2/}
}
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A. S. Atkarskaya; A. Ya. Kanel-Belov; E. B. Plotkin; E. Rips. Axiomatic definition of small cancellation rings. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 16-22. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a2/