Related papers: Small cancellation rings are non-amenable

That announcement gives the structure of totally reducible linear Lie algebras which are the Lie algebra of the holonomy group of (at least) one torsion-free connection. The result uses the (already known) classi cation of the irreducible…

We prove that a uniformly coarsely proper hyperbolic cone over a bounded metric space consisting of a finite union of uniformly coarsely connected components each containing at least two points is non-amenable and apply this to visual…

Let R be a ring and let G be a group. We prove a rather curious necessary and sufficient condition for the commutative group ring RG to be weakly nil-neat only in terms of R,G and their sections. This somewhat expands three recent results,…

It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant. Torsion-free Abelian groups of finite rank with centrally essential…

Let $A$ be an additively cancellative semialgebra over an additively cancellative semifield $K$ as defined in [9]. For a given partial action $\alpha$ of a group $G$ on an algebra, the associativity of partial skew group ring together with…

We show that an arbitrary algebra ${ A}$, (of arbitrary dimension, over an arbitrary base field and any identity is not suppose for the product), is semisimple if and only if it has zero annihilator and admits a semi-division linear basis.…

We construct in this note a unital properly infinite C*-algebra which is not K$_1$-injective.

In this paper R will denote a commutative ring with identity and M a nonzero unital R-module. We will generalize the concept of semiannihilator small submodules to the T-semiannihilator small submodules with respect to an arbitrary…

In this paper we give sufficient conditions for a free product of residually finite groups to admit an embeddable box space. This generalizes the constructions of Arzhantseva, Guentner and Spakula in arXiv:1101.1993v2 and gives a new class…

In this paper, we introduce the concept of graded m-nil clean ring to extend the existing notion of graded nil-clean ring introduced in [10]. We explore fundamental properties of these rings, emphasizing the interplay between the identity…

We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.

In line with known results on groups, we show the existence of the nilpotent radical in Lie rings with minimal condition on centralizers. We also prove a form of Engel's theorem if the characteristic is zero.

In this note we show that if $G$ is a countably infinite abelian group such that $nG=0$ for some integer $n$, then the only locally minimal group topology on $G$ is the discrete one.

In version v1 (under a different title) I was trying to give a new proof of Wedderburn's Little Theorem (WLT), stating that a finite dision ring is commutative, but I failed. So I had to withdraw the paper (version v2). Firstly I became…

We provide evidence for the Principle : Non-uniruled abelian fibrations are almost non-degenerate.

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are $p$-divisible for infinitely many primes $p$, or…

We arrange classical small cancellation constructions to produce left-orderable groups: we show that every finitely generated group is the quotient of a left-ordered small cancellation group by a finitely generated kernel (Rips…

In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…

We construct the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over compact discrete valuation rings of even residual characteristic. We also prove that the complex group algebras of $\mathrm{SL}_2$ over finite…