Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of unimodular elements in a projective module   Let $R$ be an affine algebra over an algebraically closed field of
characteristic $0$ with dim$(R)=n$. Let $P$ be a projective
$A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is
an ideal of $A$ of height $n$ such that there are two surjections
$\alpha:P\to\!\!\!\to I$ and $\phi:L\oplus A^{n-1} \to\!\!\!\to I$. Assume that
either (a) $k=1$ and $n\geq 3$ or (b) $k$ is arbitrary but $n\geq 4$ is even.
Then $P$ has a unimodular element.

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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs