Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Modules of Finite Projective Dimension   We address two aspects of finitely generated modules of finite projective
dimension over local rings and their connection in between: embeddability and
grade of order ideals of minimal generators of syzygies. We provide a solution
of the embeddability problem and prove important reductions and special cases
of the order ideal conjecture. In particular we derive that in any local ring R
of mixed characteristic p > 0, where p is a non-zero-divisor, if I is an ideal
of finite projective dimension over R and p is in I or p is a non-zero-divisor
on R/I, then every minimal generator of I is a non-zero-divisor. Hence if P is
a prime ideal of finite projective dimension in a local ring R, then every
minimal generator of P is a non-zero-divisor in R.

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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an