Proceedings of the American Mathematical Society · 1952 · 32 citations · 0 references
Natural SciencesMathematicsAlgebraPhilosophy Of MathematicsRepresentation TheoryAbstract AlgebraGroup TheoryArtin-schreier TheoryField ExtensionsSkew Fields
In this paper we shall give a necessary and sufficient condition that a skew field can be ordered; moreover, that the ordering of an ordered skew field K can be extended to an ordering of L, L being a given extension of K.The first of these two results generalizes to skew fields a theorem of E. Artin and 0. Schreier [l],1 according to which a commutative field can be ordered if and only if it is formally real.The second result generalizes in the same sense a recent theorem of J. P. Serre [2].