  In this paper we study the Freiman inequality for the minimal number of
generators of the square of an equigenerated monomial ideal. Such an ideal is
called a Freiman ideal if equality holds in the Freiman inequality. We classify
all Freiman ideals of maximal height, the Freiman ideals of certain classes of
principal Borel ideals, the Hibi ideals which are Freiman, and classes of
Veronese type ideals which are Freiman.
