  In this short note we study the entropy for algebraic actions of certain
amenable groups. The possible values for this entropy are studied. Various
fundamental results about certain classes of amenable groups are reproved using
elementary arguments and the entropy invariant. We provide a natural
decomposition of the entropy into summands contributed by individual primes and
a summand corresponding to infinity. These results extend previous work by Lind
and Ward on p-adic entropy.
