Received:

Revised:

Accepted:

Published online:

DOI:
10.5802/mrr.6

Classification: 20F67, 16S15, 16Z05

Keywords: small cancellation ring, turn, multi-turn, defining relations in rings, small cancellation group, group algebra, filtration, tensor products, Dehn’s algorithm, greedy algorithm, Gröbner basis

Author's affiliations:

Revised:

Accepted:

Published online:

Classification: 20F67, 16S15, 16Z05

Keywords: small cancellation ring, turn, multi-turn, defining relations in rings, small cancellation group, group algebra, filtration, tensor products, Dehn’s algorithm, greedy algorithm, Gröbner basis

Author's affiliations:

Agatha Atkarskaya ^{1};
Alexei Kanel-Belov ^{2};
Eugene Plotkin ^{3};
Eliyahu Rips ^{4}

@article{MRR_2021__2__1_0, author = {Agatha Atkarskaya and Alexei Kanel-Belov and Eugene Plotkin and Eliyahu Rips}, title = {Structure of small cancellation rings}, journal = {Mathematics Research Reports}, pages = {1--14}, publisher = {MathOA foundation}, volume = {2}, year = {2021}, doi = {10.5802/mrr.6}, language = {en}, url = {https://mrr.centre-mersenne.org/articles/10.5802/mrr.6/} }

TY - JOUR TI - Structure of small cancellation rings JO - Mathematics Research Reports PY - 2021 DA - 2021/// SP - 1 EP - 14 VL - 2 PB - MathOA foundation UR - https://mrr.centre-mersenne.org/articles/10.5802/mrr.6/ UR - https://doi.org/10.5802/mrr.6 DO - 10.5802/mrr.6 LA - en ID - MRR_2021__2__1_0 ER -

Agatha Atkarskaya; Alexei Kanel-Belov; Eugene Plotkin; Eliyahu Rips. Structure of small cancellation rings. Mathematics Research Reports, Volume 2 (2021), pp. 1-14. doi : 10.5802/mrr.6. https://mrr.centre-mersenne.org/articles/10.5802/mrr.6/

[1] The Burnside problem and identities in groups, Springer-Verlag, Berlin, 1979 | MR: 537580

[2] Construction of a quotient ring of ${\mathbb{Z}}_{2}\mathcal{F}$ in which a binomial $1+w$ is invertible using small cancellation methods, Groups, Algebras, and Identities (Proc. of Israel Mathematical Conferences) (Contemporary Mathematics), Volume 726 (2019), pp. 1-76 | Article | MR: 3937266 | Zbl: 07119991

[3] Group-like small cancellation theory for rings (2020), 274 pages (arXiv:2010.02836)

[4] A course on geometric group theory, 16, Mathematical Society of Japan, 2006 | Article | MR: 2243589 | Zbl: 1103.20037

[5] Geometric group theory, Colloquium Publications, Volume 63 (2018), p. 807 | MR: 3753580

[6] Infinite groups as geometric objects, Proc. of Int. Congress Math. (1983), pp. 385-392

[7] Hyperbolic Groups, 8 (1987), pp. 75-263 | MR: 919829 | Zbl: 0634.20015

[8] Finitely generated complete groups, Izv. Akad. Nauk SSSR Ser. Mat., Volume 50 (1986), pp. 883-924 | MR: 873654

[9] Diagram groups, Memoirs of the American Mathematical Society, Volume 130 (1997) no. 620, pp. 1-117 | Article | MR: 1396957 | Zbl: 0930.20033

[10] Techniques of semigroup theory, Oxford University Press, Oxford, 1992 | Zbl: 0744.20046

[11] The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput., Volume 4 (1994), pp. 1-308 | Article | MR: 1283947 | Zbl: 0822.20044

[12] On Dehn’s algorithm, Math. Ann., Volume 166 (1966), pp. 208-228 | Article | MR: 214650 | Zbl: 0138.25702

[13] Combinatorial group theory, Springer-Verlag, Berlin, 2001 (reprint of 1977 edition) | Article | Zbl: 0997.20037

[14] Infinite Burnside groups of even exponent, Izv. Math., Volume 60:3 (1996), pp. 453-654 | Article | MR: 1405529 | Zbl: 0926.20023

[15] Infinite periodic groups I, Math. USSR Izv., Volume 32 (1968), pp. 212-244 | MR: 240178

[16] Infinite periodic groups II, Math. USSR Izv., Volume 32 (1968), pp. 251-524 | MR: 240179

[17] Infinite periodic groups III, Math. USSR Izv., Volume 32 (1968), pp. 709-731 | MR: 240180

[18] An infinite group with subgroups of prime orders, Math. USSR Izv., Volume 16 (1981), pp. 279-289 | Article

[19] Groups of bounded period with subgroups of prime order, Algebra and Logic, Volume 21 (1983), pp. 369-418 | Article

[20] Geometry of defining relations in groups, Mathematics and its Applications, Volume 70 (1991), p. 505 (translated from 1989 Russian original by Yu. A. Bakhturin) | MR: 1191619

[21] Generalized small cancellation theory and applications I, Israel J. Math., Volume 41 (1982), pp. 1-146 | Article | MR: 657850 | Zbl: 0508.20017

[22] Combinatorial algebra: syntax and semantics, Springer, Cham, 2014, 355 pages

*Cited by Sources: *