  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 Gr\"obner 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. This is a short version of paper arXiv:2010.02836
