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
is a positive integer,
) over a
adic field or over a
Key Words: quaternion and symbol algebras; quadratic fields, cyclotomic fields; Kummer fields; adic fields
2010 Mathematics Subject Classification: Primary 11R52, 11R18, 11S15, 11R37, Secondary 11R04, 11A41,
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