A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in and
all the , then the equations have solutions in the
Rationals . Examples include the set of equations
with , , and Integers, and the set of equations
for rational. The trivial solution is usually not taken into account when deciding if a collection of
homogeneous equations satisfies the Hasse principle. The Hasse principle is sometimes called the
Local-Global Principle.
See also Local Field
© 1996-9 Eric W. Weisstein
1999-05-25