Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588618 | Journal of Algebra | 2007 | 17 Pages |
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