Free fields in complete skew fields and their valuations

Free Fields in Skew Fields

Building on the work of K. Chiba (J. Algebra 263 (2003), 75– 87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the universal field of fractions of a free associative algebra. Several applications to division rings generated by torsion-free nilpotent groups, skew Laurent se...

∗-Valuations and Hermitian Forms on Skew Fields

This paper is a survey of the literature on ways in which the concept of ordering can be extended to the setting of a division ring with involution and the main results for these extensions.

Small skew fields

A division ring of positive characteristic with countably many pure types is a field. Wedderburn showed in 1905 that finite fields are commutative. As for infinite fields, we know that superstable [1, Cherlin, Shelah] and supersimple [4, Pillay, Scanlon, Wagner] ones are commutative. In their proof, Cherlin and Shelah use the fact that a superstable field is algebraically closed. Wagner showed ...

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Orderings, Valuations and Hermitian Forms over ∗-fields