Abstract
We show that a formal power series ring A[[X]] over a noetherian ring A is not a projective module unless A is artinian. However, if (A, ) is any local ring, then A[[X]] behaves like a projective module in the sense that Ext p A (A[[X]], M)=0 for all -adically complete A-modules. The latter result is shown more generally for any flat A-module B instead of A[[X]]. We apply the results to the (analytic) Hochschild cohomology over complete noetherian rings.
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