Query equivalence is investigated for disjunctive aggregate
queries with negated subgoals, constants and  comparisons.
A full characterization of equivalence is given for the aggregation
functions $\COUNT$, $\MAX$, $\SUM$, $\PROD$, $\TOPTWO$ and $\PRTY$.
A related problem is that of determining, for a given natural number
$N$, whether two given queries are equivalent over all databases with
at most $N$ constants. We call this problem {\em bounded
  equivalence.\/} A complete characterization of decidability of
 bounded equivalence is given.
In particular, it is shown that this problem is decidable 
for all the above aggregation
functions as well as for $\CNTD$ (count distinct), $\STDV$ (standard 
deviation), $\MDN$ and $\AVG$.
For quasilinear queries (i.e., queries in which predicates that occur
positively are not repeated) it is shown that equivalence can be
decided in polynomial time for the aggregation functions $\COUNT$,
$\MAX$, $\SUM$, $\PROD$, $\TOPTWO$, $\PRTY$, and $\AVG$.
A similar result holds for $\CNTD$ provided that a few
additional conditions hold.
The results are couched in terms of abstract characteristics of
aggregation functions, and new proof techniques are used.
Finally, the results presented also imply that equivalence, under
bag-set semantics, is decidable for nonaggregate queries with
negation.