Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion Freeness of Schur Modules   Let $R$ be a Noetherian commutative ring and $M$ an $R$-module with
$\operatorname{pd_R} M\le 1$ that has rank. Necessary and sufficient conditions
were provided by Lebelt for an exterior power $\wedge^k M$ to be torsion free.
When $M$ is an ideal of $R$ similar necessary and sufficient conditions were
provided by Tchernev for a symmetric power $S_k M$ to be torsion free. We
extend these results to a broad class of Schur modules $L_{\lambda/\mu} M$. En
route, for any map of finite free $R$ modules $\phi\: F\rightarrow G$ we also
study the general structure of the Schur complexes $L_{\lambda/\mu}\phi$, and
provide necessary and sufficient conditions for the acyclicity of any given
$L_{\lambda/\mu}\phi$ by computing explicitly the radicals of the ideals of
maximal minors of all its differentials.

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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th