@misc{REALALG1.MIZ,
      AUTHOR = {Schwarzweller, Christoph},
      TITLE = {Ordered Rings and Fields},
      ADDRESS1 = {Institute of Informatics, University of Gdansk, Poland},
      SECTION1 = {On Order Relations},
      SECTION2 = {On Minimal Positive Indices of Polynomials},
      SECTION3 = {Preliminaries},
      SECTION4 = {Squares and Sums of Squares},
      SECTION5 = {Positive Cones and Orderings},
      SECTION6 = {Orderings vs. Order Relations},
      SECTION7 = {Some Ordered (and Non-ordered) Rings},
      SECTION8 = {Ordered Polynomial Rings},
      DAY = {17},
      MONTH = {March},
    YEAR = {2017},
      SUMMARY = {We introduce ordered rings and fields
      following Artin-Schreier's approach using
      positive cones. We show that such orderings coincide with total order
      relations and give examples of ordered (and non ordered) rings and fields.
      In particular we show that polynomial rings can be ordered in (at least)
      two different ways \cite{Pre84,KS89,Jac64,Rad91}.}}

@BOOK{Pre84,
      AUTHOR = {Alexander Prestel},
      TITLE = {Lectures on Formally Real Fields},
      PUBLISHER = {Springer Verlag},
      YEAR = {1984}}

@BOOK{KS89,
      AUTHOR = {Manfred Knebusch and Claus Scheiderer},
      TITLE = {Einf\"{u}hrung in die reelle Algebra},
      PUBLISHER = {Vieweg Verlag},
      YEAR = {1989}}

@BOOK{Jac64,
      AUTHOR = {Nathan Jacobson},
      TITLE = {Lecture Notes in Abstract Algebra,
               III. Theory of Fields and Galois Theory},
      PUBLISHER = {Springer Verlag},
      YEAR = {1964}}

@BOOK{Rad91,
      AUTHOR = {Knut Radbruch},
      TITLE = {Geordnete K\"{o}rper},
      PUBLISHER = {Lecture Notes, University of Kaiserslautern, Germany},
      YEAR = {1991}}
