  The aim of this paper is to study certain properties of the Kullback-Leibler
distance between two positive integer numbers or between two ideals. We present
some results related the entropy of a positive integer number and the
divergence of two numbers. We also study the entropy of some types of ideals
and the divergence of two ideals. Finally, we find some inequalities, involving
the entropy H of an exponential divisor of a positive integer, respectively the
entropy H of an exponential divisor of an ideal.
