For any algebra C over a
commutative ring k Sweedler defined a cohomology set which generalizes Amitsur’s
second cohomology group H2(C∕k). Any Sweedler C-two-cocycle σ gives rise to a
change of rings functor ()σ from the category of C-bimodules to the category of
Cσ-bimodules, where Cσ is the k-algebra with multiplication altered by
σ, which in turn induces a map ϕn(σ,M) : Hn(C,M) → Hn(Cσ,Mσ) on
Hochschild cohomology for any C-bimodule M and any positive integer n. In this
paper, several properties of ϕn(σ,M) are derived, including: If C is a finite
dimensional algebra over a field k, ϕ1(σ,M) is an injection for all σ and
M.
