D sets and IP rich sets in countable, cancellative abelian semigroups

We give combinatorial characterizations of IP rich sets (IP sets that remain IP upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultrafilters, all of whose members have positive upper Banach density) in a general countable, cancellative abelian semigroup. We then show that the family of IP rich sets strictly contains the family of D sets.