# Pseudo-Sylvester domains and skew laurent polynomials over firs

@article{Henneke2020PseudoSylvesterDA, title={Pseudo-Sylvester domains and skew laurent polynomials over firs}, author={F. Henneke and Diego L'opez-'Alvarez}, journal={arXiv: Rings and Algebras}, year={2020} }

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

## References

SHOWING 1-10 OF 52 REFERENCES

### Free division rings of fractions of crossed products of groups with Conradian left-orders

- MathematicsForum Mathematicum
- 2020

<jats:p>Let <jats:italic>D</jats:italic> be a division ring of fractions of a crossed product <jats:inline-formula id="j_forum-2019-0264_ineq_9999">
…

### Projective modules over Laurent polynomial rings

- Mathematics
- 1978

Quillen's solution of Serre's problem is extended to Laurent polynomial rings. An example is given of a A[T, r~']-module P which is not extended even though A is regular and Pm is extended for all…

### Localization: On Division Rings and Tilting Modules

- Mathematics
- 2008

Let G be a locally indicable group, k a division ring, and kG a crossed-product group ring, In [Hug70], Ian Hughes proved that, up to kG-isomorphism, at most one division ring of fractions of kG…

### Localization, Whitehead groups and the Atiyah conjecture

- Mathematics
- 2018

Let Wh^w(G) be the K_1-group of square matrices over the integral group ring ZG which are not necessarily invertible but induce weak isomorphisms after passing to Hilbert space completions. Let D(G)…

### The Farrell–Jones conjecture for normally poly-free groups

- Mathematics
- 2019

We prove the $K$- and $L$-theoretic Farrell--Jones Conjecture with coefficients in an additive category for every normally poly-free group, in particular for even Artin groups of FC-type, and for all…

### The Ore condition, affiliated operators, and the lamplighter group

- Mathematics
- 2002

Let G be the wreath product of Z and Z/2, the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore…

### Algebraic K-theory

- Mathematics
- 2005

The idea will be to associate to a ring R a set of algebraic invariants, Ki(R), called the K-groups of R. We can even do a little better than that: we will associated an (infinite loop) space K(R) to…

### Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory.

- Mathematics
- 1998

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of…

### The strong Atiyah and Lück approximation conjectures for one-relator groups

- MathematicsMathematische Annalen
- 2019

It is shown that the strong Atiyah conjecture and the Lück approximation conjecture in the space of marked groups hold for locally indicable groups. In particular, this implies that one-relator…