Group-like Small Cancellation Theory for Rings

Авторы: Atkarskaya A., Kanel-Belov A., Plotkin E., Rips E.
Сборник: ArXiv
Серия: Series arxive "math"
Том: 2005
Год издания: 2020
Издательство: Cornell University Press
Местоположение издательства: United States
Аннотация: The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining relations. The relations must satisfy three types of axioms. The major one among them is called the Small Cancellation Axiom. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. It turns out that the defined ring possesses a kind of Gröbner basis and a greedy algorithm. Finally, this ring can be used as a first step towards the iterated small cancellation theory which hopefully plays a similar role in constructing examples of rings with exotic properties as small cancellation groups do in group theory.
Добавил в систему: Белов Алексей Яковлевич

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