Article ID Journal Published Year Pages File Type
4588618 Journal of Algebra 2007 17 Pages PDF
Abstract

A field k of characteristic unequal to 2 is called tractable if for every nonzero ai,bi∈k, i=1,2,3, whenever the quaternion algebra (ai,bj/k) is split for all i≠j and (a1,b1/k)≅(a2,b2/k)≅(a3,b3/k), then (ai,bi/k) is split. In the present paper, we study tractability of algebraic function fields in one variable over global fields and give specific examples of tractable function fields and intractable function fields of genus one over Q, the rationals.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory