Building on recent work of Jaikin-Zapirain, we provide a homological criterion for ring to be pseudo-Sylvester domain, that is, admit division fractions over which all stably full matrices become invertible. We use the study skew Laurent polynomial rings free ideal (firs). As an application our methods, prove crossed products with free-by-{infinite cyclic} and surface groups are domains uncondi...

In this work, linearized multivariate skew polynomials over division rings are introduced. Such right linear the corresponding centralizer and generalize polynomial finite fields, group or differential rings. Their natural evaluation is connected to remainder-based of free polynomials. It shown that P-independent sets those given by linearly independent when partitioned into conjugacy classes. ...

Given a Hilbertian field k and finite set S of Krull valuations , we show that every split embedding problem G → Gal ( L / ) over with abelian kernel has solution F such v ∈ is totally in . Two applications are then given. Firstly, solve non-constant variant the Beckmann–Black for solvable groups: given non-trivial group Galois extension shown to occur as specialization at some t 0 E T ⊈ ‾ Seco...

We consider polynomial maps of the form f(z,w) = (p(z), q(z,w)) that extend as holomorphic maps of CP. Mattias Jonsson introduces in “Dynamics of polynomial skew products on C2” [Math. Ann., 314(3): 403– 447, 1999] a notion of connectedness for such polynomial skew products that is analogous to connectivity for the Julia set of a polynomial map in one-variable. We prove the following dichotomy:...