The structure of small cancellation groups is well known. Тhey are widely used in construction of groups with unusual properties (for example Burnside groups and Tarskii monster). We were interested in developing a similar theory for rings. However, such theory meets significant difficulties because, unlike groups, rings have two operations: addition and multiplication. I will speak about small cancellation conditions for rings that we introduced. These conditions provide the desired properties. I will discuss our way towards these conditions, examples and possible applications of small cancellation rings.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
