Research work · 1949
On ordered division rings
B. Neumann
Transactions of the American Mathematical Society
Abstract
Table of Contents Part I. Embedding an ordered group in a division ring. 1. Introduction.202 2. Archimedean classification in an ordered semigroup.204 3. Well-ordered sequences in an ordered semigroup.206 4. Formal power series over a ring.209 5. Formal power series division rings.211 6. Appendix.A theorem on the group ring of a free group.213 Part II.Embedding the real numbers in an ordered division ring.7. Introduction.215 8. Preliminaries and notation.217 9. Algebraic adjunction of an element.218 10.Ordering a simple transcendent extension.223 11.Relative orders of magnitude and alternators.228 12. Rate of change of a polynomial and approximations of roots.230 13.Product polynomials and higher alternators.232 14.Degree of approximation to a root.235 15.Comparison of polynomials near a root.240 16.Ordering a simple algebraic extension (in 9Î).245 17.Ordering a simple algebraic extension (outside ^9t).250 Bibliography.252 Part I. Embedding an ordered group in a division ring