3 citations · 6 across the 5 of their papers we have counts for
5 papers
The Burnside problem for odd exponents
Agatha Atkarskaya, Eliyahu Rips, Katrin Tent
We show that the free Burnside groups are infinite for and odd , the best currently known lower bound for the exponent. The proof uses iterated small…
Small cancellation rings are non-amenable
Agatha Atkarskaya
In this paper we prove that small cancellation rings under some natural restrictions are non-amenable and contain non-commutative free associative algebra.
Group-like small cancellation theory for rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free gr…
Small cancelation rings
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
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…
Construction of a quotient ring of in which a binomial is invertible using small cancellation methods
A. Atkarskaya, A. Kanel-Belov, E. Plotkin +1
We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring , where $\mathbb{Z}_2\mathc…