Pseudo-Sylvester domains and skew laurent polynomials over firs

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



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