  An algebraic integer is said large if all its real or complex embeddings have
absolute value larger than $1$. An integral ideal is said \emph{large} if it
admits a large generator. We investigate the notion of largeness, relating it
to some arithmetic invariants of the field involved, such as the regulator and
the covering radius of the lattice of units. We also study its connection with
the Weil height and the Bogomolov property. We provide an algorithm for testing
largeness and give some applications to the construction of floor functions
arising in the theory of continued fractions.
