Diana Savin : About split quaternion algebras over quadratic fields and symbol algebras of degree $n$, 307-312


In this paper we determine sufficient conditions for a quaternion algebra to split over a quadratic field. In the last section of the paper, we find a class of non-split symbol algebras of degree $n$ (where $n$ is a positive integer, $n\geq 3$) over a $p-$ adic field or over a cyclotomic field.

Key Words: quaternion and symbol algebras; quadratic fields, cyclotomic fields; Kummer fields; $p-$ adic fields

2010 Mathematics Subject Classification: Primary 11R52, 11R18, 11S15, 11R37, Secondary 11R04, 11A41, 11F85.