Related papers: Small cancellation rings are non-amenable

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 group and introduce three axioms for the corresponding…

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…

We prove that cancellation of reflexive modules over affine rings holds under some restrictions. We construct examples to show that this is false even over polynomial rings without the extra assumptions.

We introduce and study a relative cancellation property for associative algebras. We also prove a characterization result for polynomial rings which partially answers a question of Kraft.

The purpose of this paper is to prove that certain limits of polynomial rings are themselves polynomial rings, and show how this observation can be used to deduce some interesting results in commutative algebra. In particular, we give two…

It is shown that the reduced C*-algebra of a nontrivial linear group $\Gamma<GL_{d}(k)$ with trivial amenable radical is selfless. Thus selflessness and simplicity coincide for reduced C*-algebras of linear groups. Similar results are…

We extend fundamental results of small cancellation theory to groups whose presentations satisfy the generalizations of the classical C(6) and C(7) conditions in graphical small cancellation theory. Using these graphical small cancellation…

Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.

We call a simplicial complex algebraically rigid if its Stanley-Reisner ring admits no nontrivial infinitesimal deformations, and call it inseparable if does not allow any deformation to other simplicial complexes. Algebraically rigid…

We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of…

We give two equivalent definitions of sigma algebras that are atomless conditionally to a smaller sigma algebra.

Let $\mf{g}$ be any finite-dimensional Lie algebra with Killling form $B$. Let $\mf{h}$ be a subalgebra of $\mf{g}$ on which the Killing form is non degenerate. Then $\mf{h}$ is reductive.

We exhibit a non-constructive proof in which anti-automorphisms are not valuation-preserving and hence non-isometric

This paper introduces and studies nil-reversible rings wherein we call a ring R nil-reversible if the left and right annihilators of every nilpotent element of R are equal. Reversible rings (and hence reduced rings) form a proper subclass…

Let $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is endowed with a descending filtration indexed on an ordered group $(G,<)$ such that the restriction to $k$ is positive. We show that the existence of free algebras on a…

It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a questioned original posed in a paper on a taxonomy of 2-primal rings. Answers to similar questions on minimal rings relating to this taxonomy…

We prolonge the list of C*-algebras for which all extensions by any stable separable C*-algebra are semi-invertible. In particular, we handle certain amalgamations, both of C*-algebras and of groups. Concerning groups we consider both…

We develop a general ring theory in the o-minimal setting culminating in a description of all the definable rings in an arbitrary o-minimal structure. We show that every definably connected ring with non-trivial multiplication defines an…

We give a simplified approach to the cubulation of small-cancellation quotients of free products of cubulated groups. We construct fundamental groups of compact nonpositively curved cube complexes that do not virtually split.