Small cancellation rings and Groebner-Shirshov bases

Small cancellation groups and their generalisations give a big source of groups with exotic properties (e.g. Burnside groups, Tarskii monster, finitely generated non-finitely presented subgroups of finitely presented groups, aka Rips construction, etc.) I will speak about a similar theory for algebras, which was recently developed. We expect that it can be used for constructing algebras with exotic properties as small cancellation groups are used for group-theoretic examples. On the other hand, a technique that we developed is of its own interest and can be considered as a generalisation of Groebner-Shirshov bases.

The talk is based on joint work with A. Kanel-Belov, E. Plotkin and E. Rips.

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