@article{Graeter2020,
  author    = {Gr{\"a}ter, Joachim},
  title     = {Free division rings of fractions of crossed products of groups with Conradian left-orders},
  series = {Forum mathematicum},
  volume    = {32},
  journal   = {Forum mathematicum},
  number    = {3},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0933-7741},
  doi       = {10.1515/forum-2019-0264},
  pages     = {739 -- 772},
  year      = {2020},
  abstract  = {Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field.},
  language  = {en}
}
@article{BrungsGraeter2017,
  author    = {Brungs, Hans H. and Gr{\"a}ter, Joachim},
  title     = {On central extensions of SL(2, F) admitting left-orderings},
  series = {Journal of Algebra},
  volume    = {486},
  journal   = {Journal of Algebra},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-8693},
  doi       = {10.1016/j.jalgebra.2017.05.025},
  pages     = {288 -- 327},
  year      = {2017},
  abstract  = {For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups.},
  language  = {en}
}
@article{GraeterWirths2015,
  author    = {Gr{\"a}ter, Joachim and Wirths, Karl-Joachim},
  title     = {On Elementary Bounds for Sigma(infinity)(k=n)k(-s)},
  series = {The American mathematical monthly : an official publication of the Mathematical Association of America},
  volume    = {122},
  journal   = {The American mathematical monthly : an official publication of the Mathematical Association of America},
  number    = {2},
  publisher = {Mathematical Assoc. of America},
  address   = {Washington},
  issn      = {0002-9890},
  doi       = {10.4169/amer.math.monthly.122.02.155},
  pages     = {155 -- 158},
  year      = {2015},
  abstract  = {By means of elementary arguments, we derive lower and upper bounds for the infinite series Sigma(infinity)(k=n)k(-s), s is an element of R and s > 1.},
  language  = {en}
}
@article{GraeterWeese2004,
  author    = {Gr{\"a}ter, Joachim and Weese, Martin},
  title     = {On the norm equation over function fields},
  issn      = {0024-6107},
  year      = {2004},
  abstract  = {If K is an algebraic function field of one variable over an algebraically closed field k and F is a finite extension of K, then any element a of K can be written as a norm of some b in F by Tsen's theorem. All zeros and poles of a lead to zeros and poles of b, but in general additional zeros and poles occur. The paper shows how this number of additional zeros and poles of b can be restricted in terms of the genus of K, respectively F. If k is the field of all complex numbers, then we use Abel's theorem concerning the existence of meromorphic functions on a compact Riemarm surface. From this, the general case of characteristic 0 can be derived by means of principles from model theory, since the theory of algebraically closed fields is model-complete. Some of these results also carry over to the case of characteristic p > 0 using standard arguments from valuation theory},
  language  = {en}
}
@article{BrungsGraeter2000,
  author    = {Brungs, Hans and Gr{\"a}ter, Joachim},
  title     = {Trees and Valuation Rings},
  year      = {2000},
  language  = {en}
}
@article{GraeterKlein2000,
  author    = {Gr{\"a}ter, Joachim and Klein, Markus},
  title     = {The Principal Axis Theorem for Holomorphic Functions},
  year      = {2000},
  language  = {en}
}
@article{BrungsGraeter1996,
  author    = {Brungs, Hans and Gr{\"a}ter, Joachim},
  title     = {Orders of Higher Rank in Semisimple Artinian Rings},
  year      = {1996},
  language  = {en}
}
@article{Graeter1996,
  author    = {Gr{\"a}ter, Joachim},
  title     = {Algebraic elements in division rings},
  year      = {1996},
  language  = {en}
}
@article{Graeter1996,
  author    = {Gr{\"a}ter, Joachim},
  title     = {Extending valuation rings via ultrafilters},
  year      = {1996},
  language  = {en}
}