Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry of extending properties in nonsingular Utumi rings   This paper presents the right-left symmetry of the CS and max-min CS
conditions on nonsingular rings, and generalization to nonsingular modules. We
prove that a ring is right nonsingular right CS and left Utumi if and only if
it is left nonsingular left CS and right Utumi. A nonsingular Utumi ring is
right max (resp. right min, right max-min) CS if and only if it is left min
(resp. left max, left max-min) CS. In addition, a semiprime nonsingular ring is
right max-min CS with finite right uniform dimension if and only if it is left
max-min CS with finite left uniform dimension.

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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg