  The Kunneth trick is a formula for the top cohomology of the derived tensor
product of two complexes of modules over a ring.
  In this note we present two improvements of this formula. The first improved
Kunneth trick is a formula for the top cohomology of the plain tensor product
of two DG modules over a nonpositive DG ring. The second trick handles the
derived tensor product of two DG modules over a nonpositive DG ring. The proofs
are elementary.
