Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power series rings and projectivity   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 $(A,{\mathfrak
m})$ is local, then $A[[X]]$ behaves like a projective module in the sense that
$Ext^p_A(A[[X]], M)=0$ for all ${\mathfrak m}$-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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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom