Let Λ be a radical-square zero algebra over an algebraically closed field k with radical r and Γ = Λ/r 0 r Λ/r ! be the associated hereditary algebra. There is a well-known functor F : modΛ→modΓ which induces a stable equivalence. We show that the functor F keeps Gabriel-Roiter measures and Gabriel-Roiter factors. Thus one may study the Gabriel-Roiter measure for Λ using F and known facts for h...

In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts X ⊂ {0, 1}Z: for every infinite subset L ⊆ Z there exists an infinite subset K ⊆ L such that πK(X) is a countable subset of {0, 1}K . The notion of eventual fragmentability is one of the...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

The notion of thin sums matroids was invented to extend the notion of representability to non-finitary matroids. A matroid is tame if every circuit-cocircuit intersection is finite. We prove that a tame matroid is a thin sums matroid over a finite field k if and only if all its finite minors are representable over k. We expect that the method we use to prove this will make it possible to lift m...

In this paper it is established that all two-dimensional polynomial automorphisms over a Dedekind Q-algebra are stably tame; in fact, they become tame with the addition of three more dimensions. A key element in the proof is this additional new theorem: Over an Artinian Q-algebra all two-dimensional polynomial automorphisms having Jacobian determinant one are tame.

Marden conjectured that a hyperbolic 3-manifold M with finitely generated fundamental group is tame, i.e. it is homeomorphic to the interior of a compact manifold with boundary [42]. Since then, many consequences of this conjecture have been developed by Kleinian group theorists and 3-manifold topologists. We prove this conjecture in theorem 10.2, actually in slightly more generality for PNC ma...

Let A be the path algebra of a Euclidean quiver over a finite field k. The aim of this paper is to classify the modules M with the property [M ] ∈ C(A), where C(A) is Ringel’s composition algebra. Namely, the main result says that if |k| 6= 2, 3, then [M ] ∈ C(A) if and only if the regular direct summand of M is a direct sum of modules from non-homogeneous tubes with quasi-dimension vectors non...

Let K be a field of characteristic zero. We characterize coordinates and tame coordinates in K[z][x,y], i.e. the images of x respectively under all automorphisms and under the tame automorphisms of K[z][x,y]. We also construct a new large class of wild automorphisms of K[z][x,y] which maps x to a concrete family of nice looking polynomials. We show that a subclass of this class is stably tame, ...