  Freiman's theorem gives a lower bound for the cardinality of the doubling of
a finite set in $\RR^n$. In this paper we give an interpretation of his theorem
for monomial ideals and their fiber cones. We call a quasi-equigenerated
monomial ideal a Freiman ideal, if the set of its exponent vectors achieves
Freiman's lower bound for its doubling. Algebraic characterizations of Freiman
ideals are given, and finite simple graphs are classified whose edge ideals or
matroidal ideals of its cycle matroids are Freiman ideals.
