Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolutions of length four which are Differential Graded Algebras   Let $P$ be a commutative Noetherian ring and $F$ be a self-dual acyclic
complex of finitely generated free $P$-modules. Assume that $F$ has length four
and $F_0$ has rank one. We prove that $F$ can be given the structure of a
Differential Graded Algebra with Divided Powers; furthermore, the
multiplication on $F$ exhibits Poincar\'e duality. This result is already known
if $P$ is a local Gorenstein ring and $F$ is a minimal resolution. The purpose
of the present paper is to remove the unnecessary hypotheses that $P$ is local,
$P$ is Gorenstein, and $F$ is minimal.

34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an